







A circle, a point, and a tangent line 
20191231 

From Faisal: A circle has radius 10 units and passes through the point (5,16). The xaxis is a tangent to the circle. Find the possible equations of circle? Answered by Penny Nom. 





A tangent line to a parabola 
20151202 

From pei: Given that the line y=mx5 is a tangent to the curve y=2x^2+3 find the positive value of M. Answered by Penny Nom. 





A tangent line to a circle 
20150903 

From Jamie: Use the Greek method to find an equation of the tangent line to the circle
x^2+y^24x+6y+4=0 at the points (3,2square root 23. Answered by Penny Nom. 





A tangent to y = x^3 
20150531 

From Brayden: Show that a tangent line drawn to the curve y=x^3 at the point (d,f (d)), where d>0, forms a right triangle with the x and y axes in quadrant 4 whose area is (2/3)d^4. Answered by Penny Nom. 





A tangent to y=x^3 passes through (0,2) 
20150405 

From Kevin: Given that the curve y=x^3 has a tangent line that passes through point (0,2). Find the equation of the tangent line Answered by Penny Nom. 





A tangent to a curve passing through a point not on the graph 
20140915 

From Aquilah: For the curve y = x2 + 3x, find the equations of all tangent lines for this graph
that also go through the point (3, 14). Answered by Penny Nom. 





A tangent of the curve (x/a)^n+(y/b)^n =2 
20140415 

From sudhir: the equation of tangent of the curve (x/a)^n+(y/b)^n =2. at(a,b) is Answered by Penny Nom. 





Tangents to the curve y = x^3 
20130324 

From Ethan: How many tangent lines to the curve y = x^33 pass through the
point (2, 4)? For each such line, and the exact coordinates of the point of
tangency on the curve. Answered by Penny Nom. 





A tangent to f(x) = 1/x 
20120904 

From Steven: Consider the graph of the function f(x) = 1/x in the first quadrant, and a line tangent to f at a point P where x = k. Find the slop of the line tangent to f at x = k in terms of k and write an equation for the tangent line l in terms of k. Answered by Penny Nom. 





An equilateral triangle and some circles 
20120110 

From tushar: draw an equilateral triangle with side 6cm.draw 3circles with radii 3cm on each angular point of triangle.draw common tangent on each of two circles Answered by Penny Nom. 





Lines tangent to y^2=4x 
20111111 

From Reuchen: Find equations of the lines tangent to y^2=4x and containing (2,1). Answered by Penny Nom. 





A line tangent to f(x)=1/x 
20110605 

From Michael: A line tangent to f(x)=1/x in the first quadrant creates a right triangle
with legs the xaxis and the yaxis. Prove that this triangle is always
2 square units regardless of where the point of tangency is. Answered by Penny Nom. 





A tangent line 
20110103 

From Amanda:
Question from Amanda, a student:
an equation of the line tangent to y=x^3+3x^2+2 at its point of inflection is
(A) y=6x6
(B) y= 3x+1
(C) y= 2x+10
(D) y=3x1
(E) y=4x+1 Answered by Penny Nom. 





A tangent line to a circle 
20100415 

From Rhonda: The Greek method for finding the equation of the tangent line to a circle used the fact that at any point on a circle the line containing the reauis and the tangent line are perpendicular. Use this method to find an equation of the tangent line to the circle x^2+y^2=9 at the point (1,2 square root of 2). Answered by Penny Nom. 





A point on 8x^2+5xy+y^3=149 
20090204 

From Vivian: Consider the curve defined by 8x2+5xy+y3=149
a) find dy/dx
b) Write an equation for the line tangent to the curve at the point (4,1)
c) There is a number k so that the point (4.2,k) is on the curve. Using the tangent line found in part b), approximate the value of k.
d) write an equation that can be solved to find the actual value of k so that the point (4.2,k) is on the curve
e) Solve the equation found in part d) for the value of k Answered by Harley Weston. 





Tangent line 
20081027 

From Maddie: Find a general equation for a line that touches, but does not pass through the function Y=X2(X squared) + BX+C. Answered by Stephen La Rocque and Victoria West. 





The slope of a tangent line 
20081018 

From Amanda: If f(x)=square root of (x+4), and the slope of the tangent line at x=21 was 1/n for some integer n, then what would you expect n to be? Answered by Stephen La Rocque. 





A tangent line to f(x) = 1/(x  1) 
20081016 

From Amanda: If f(x)=1/(x1) then what is the slope of the tangent line at x=2? Answered by Harley Weston. 





A tangent to a circle 
20080906 

From Jake: Find an equation of the line that is tangent to the circle x^2 + y^2 = 3 at the point (1,√2) Answered by Penny Nom. 





A particle moves in the xyplane 
20071112 

From Russell: A particle moves in the xyplane with
X = 2t^3  12t^2 + 18t
Y = 3t^4  28t^3 + 72t^2
find an equation of the line tangent to the given curve at t_0_ = 1
note: t_0_ is t subscript 0 Answered by Harley Weston. 





Equation of a tangent line to a function 
20071004 

From Princess: If f ' (x) = 3x^2 +1, find the equation of
the tangent line to f(x) = x^3 + x at x= 1. Answered by Stephen La Rocque. 





Twocolumn proof for a circle geometry problem 
20070824 

From Kendra: i have to prove that tangents to a circle at the endpoints of a diatmeter are parallel by stating whats given, whats to prove and a plane, then write a two column proof i dont understand this Answered by Stephen La Rocque. 





Circle Geometry 
20070814 

From Robin: In a triangle ABC, angle A=75 and B=60. A circle circumscribes the triangle. The tangents of the at points A and B meet in a point D outside the circle. Show that ABD is an isosceles triangle with a right angle at D. Diagram included. Answered by Stephen La Rocque. 





Two tangent lines to y=x^3 
20070607 

From stephanie: find the equations of two tangent lines to the y=x^3 function through the point (2,8) Answered by Penny Nom. 





A common tangent line 
20070220 

From chris: I have this problem I have been working on for days and cannot figure it out. it states: Find the two points on the curve y=x^4  2x^2  x that have a common tangent line.
I know you use the first derivative to find the tangent line so if it is a common tangent line should you find two of the exact same tangent line equations at two coordinate points? Answered by Chris Fisher. 





The tangent line at an inflection point 
20041128 

From Louise: the equation of the tangent line to the curve y = x^{3}  6x^{2} at its point of inflection is... Answered by Penny Nom. 





The sketch of a graph 
20031007 

From A student: I was wondering how do you figure out if a graph has a horizontal tangent line. One of my homework problem was to sketch the graph of the following function; (4/3)x^{3}2x^{2}+x. I set f''(x) ( the second derivative) of the function equal to zero and got the inflection point:(1/2,1/6). Also i am having trouble finding the concavity for x>1/2 and x<1/2, i am getting a different answer from the back of the book, the graph i draw looks completely different from the correct answer. Answered by Penny Nom. 





The slope of a tangent line 
20020304 

From Ridley: Suppose a function f(x) has the line 3x+4y=2 as its tangent line at x=5. Find f'(5). Answered by Harley Weston. 





A tangent line 
20011121 

From A student: write an equation of the line tangent to the graph of
e^{y} + ln(xy) = 1 + e at (e,1) Answered by Harley Weston. 

