JEE MainMathematicsModerateEllipse

Let (m, n) to be a point from which two perpendicular tangents
can be drawn to the ellipse
4x^2 + 5y^2 = 20. If E=4m + 3n, then

Show answer and solution

Here, (m, n) lies on director circle of given ellipse

\left( \frac{x^{2}}{5} + \frac{y^{2}}{4} = 1 \right)

;gka (m,n) nh?kZo`Ùk

\left( \frac{x^{2}}{5} + \frac{y^{2}}{4} = 1 \right)

o`Ùk ij
fLFkr

\therefore\left( m^{2} + n^{2} = 5 + 4 \right) \Rightarrow \

Director
circle fu;ked o`Ùk

\therefore m = 3cos\theta n = 3sin\theta

E = 12cos\theta + 9sin\theta

- \sqrt{(12)^{2} + 9^{2}} \leq E \leq \sqrt{(12)^{2} - 9^{2}}

- 15 \leq E \leq 15

Source: Grass-G / M-26 Mathematics Paper 1 15 Jan.docx

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