Question

The equation of the tangents to the ellipse 9x² + 16y² = 144 from the point (2, 3) are–

• A. y = 3, x + y = 5
• B. y = 3, x = 2
• C. y = 2, x = 3
• D. y = 3, x = 5

Answer 1

Answer: (A)

y = 3, x + y = 5

Answer 2

$\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1$ .... (1)

̃ $\left\{ \begin{matrix} a^{2} = 16 \\ b^{2} = 9 \end{matrix} \right.\$ P(2, 3)

Q point P lies outside the ellipse (1)

\ Eq of tangent in slope form

̃ y = mx ± $\sqrt{a^{2}m^{2} + b^{2}}$

̃ y = mx ± $\sqrt{16m^{2} + 9}$ ....(2)

Now, line (2) is passing through the point P.

\ 3 = 2m ± $\sqrt{16m^{2} + 9}$ ̃ m = ?

Put the value of M in equation (2)