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 Question from Andrew, a student: What is the equation of the line tangent to the circle with equation x^2+y^2=25 at the point (-4,3)

Hi Andrew,

The key to this problem is that if $C$ is the centre of a circle and $P$ is a point on the circle then the tangent to the circle at $P$ and the radius $CP$ are perpendicular.

What is the centre $C$ of the circle $x^2+y^2=25?$

What is the slope of the line segment from $C$ to $P(-4,3)?$

What is the slope of the tangent to the circle at $P?$

What is the equation of this tangent?

Penny

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