If m is the gradient of the tangent from the point (3,2)to the ellipse 9x^2 + 16y^2 = 144, find aquadratic equation in m, By noting whether the roots ofthis equation are real or imaginary, determine ifthe point (3,2) lies within the ellipse.

kokomocutie88r1

kokomocutie88r1

Answered question

2022-07-26

If m is the gradient of the tangent from the point (3,2)to the ellipse 9 x 2 + 16 y 2 = 144, find aquadratic equation in m, By noting whether the roots ofthis equation are real or imaginary, determine ifthe point (3,2) lies within the ellipse.

Answer & Explanation

Wayne Everett

Wayne Everett

Beginner2022-07-27Added 19 answers

Eqn of any tangent to the ellipse is y=mx +squre root of a 2 m 2 + b 2 this passes through (3,2) 2=3m + sqrt of 16 m 2 + 9
2-3m=sqrt of 16 m 2 + 9
Squaring on both sides we get 7 m 2 12 m + 5 = 0
(7m-5)(m-1)=0
M=1or m=5/7
If point lies inside ellipse we can not draw the the tangents

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