Prove that the radius of the circle with equation x² + y² = 25 is perpendicular on the tangent line in P(3,4) to the circle? Thank you!
2 Answers
The slope of the Tangent line is
Explanation:
Use the equations and slopes of the Radius and the Tangent line.
For the Radius whose end points are the center
The slope is
For the Tangent line at
Determine the slope by differentiating
Let
By the given point
The slope of the Tangent line is
I hope the explanation is useful...God bless.
See below
Explanation:
Given
We know this is a circle centered in
The given point belongs to circle because
The derivative is
By other hand the vector defined by
We know that two vectors are penperdiclar if the product of tangents of their angles is
But