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(a) Prove that the equation of the tangent line at the point T(x0,Yo) on the circle S(x, y) = x² + y² + 2gx + 2fy + c = 0 is given by S(x; xo,y; Yo) = xx, + yyo + g(x + xo) + f (y + Yo) + c = 0. (b) If a point A(x',y') is any point, prove that A is inside, on or outside the circle S(x,y) = 0 if and only if S(x',y') § 0. (c) Find the equation of the tangent lines from the point A(-1,3) to the circle x² + y² – 4x – 5 = 0.

(a) Prove that the equation of the tangent line at the point T(x0,Yo) on the circle S(x, y) = x² + y² + 2gx + 2fy + c = 0 is given by S(x; xo,y; Yo) = xx, + yyo + g(x + xo) + f (y + Yo) + c = 0. (b) If a point A(x',y') is any point, prove that A is inside, on or outside the circle S(x,y) = 0 if and only if S(x',y') § 0. (c) Find the equation of the tangent lines from the point A(-1,3) to the circle x² + y² – 4x – 5 = 0.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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Q4 (a) Prove that the equation of the tangent line at the point T(xo,Yo) on the circle S(x, y) = x² + y² + 2gx + 2fy +c = 0 is given by S(x; x0,y; Yo) = xx, + yyo + g(x + xo) + f (y + y) + c = 0. (b) If a point A(x',y') is any point, prove that A is inside, on or outside the circle S(x,y) = 0 if and only if S(x',y') § 0. (c) Find the equation of the tangent lines from the point A(-1,3) to the circle x? + y² – 4x – 5 = 0.
Transcribed Image Text:Q4 (a) Prove that the equation of the tangent line at the point T(xo,Yo) on the circle S(x, y) = x² + y² + 2gx + 2fy +c = 0 is given by S(x; x0,y; Yo) = xx, + yyo + g(x + xo) + f (y + y) + c = 0. (b) If a point A(x',y') is any point, prove that A is inside, on or outside the circle S(x,y) = 0 if and only if S(x',y') § 0. (c) Find the equation of the tangent lines from the point A(-1,3) to the circle x? + y² – 4x – 5 = 0.
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