Equation of Circle and Tangents: A, B are points on circle w/ equation x^2 + y^2 = 25

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sojeee

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A and B are points on the circle with equation x2 + y2 = 25
A is (3,4)
B is a point on the y - axis, with coordinates (0,-5)
PA and PB are tangents.

P is the point where PA and PB both come from. Work out the coordinates.
 
sojeee said:
A and B are points on the circle with equation x2 + y2 = 25
A is (3,4)
B is a point on the y - axis, with coordinates (0,-5)
PA and PB are tangents.

P is the point where PA and PB both come from. Work out the coordinates.
Click to expand...

1) Please give P an address.
2) Write the equation of PA, given the two points, P and A.
3) Write the equation of PB, given the two points, P and B.
4)

You are well on your way.
 
Last edited:
sojeee said:
A and B are points on the circle with equation x2 + y2 = 25
A is (3,4)
B is a point on the y - axis, with coordinates (0,-5)
PA and PB are tangents.

P is the point where PA and PB both come from. Work out the coordinates.
Click to expand...

As I read this, it's defining P as the intersection of the tangents at A and B. You need to find the slope of each tangent, and use that and the point to write an equation of the line. Then you can find the intersection, which is P.

This can be simplified somewhat because the tangent at B is very simple, so you may not need to actually solve an equation.

If you want further help, you must show us some work, or at least tell us what you do or do not understand. As it is, we can't be sure what methods you are expected to use. (The slopes could be found by calculus, or by geometry, or by algebra.)
 
sojeee said:
A and B are points on the circle with equation x2 + y2 = 25
A is (3,4)
B is a point on the y - axis, with coordinates (0,-5)
PA and PB are tangents.

P is the point where PA and PB both come from. Work out the coordinates.
Click to expand...
If (a,b) is a point on the circle, then the slope of the tangent at (a,b) is -a/b. This is the main piece you need. Now find the equation of both lines (for each line you have a point-it was given- and know you can compute the slope. Continue....
 
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