If the tangents on the ellipse 4x2 + y2 = 8 at the points (1, 2) and (a, b) are perpendicular to each other, then a2 is equal to

Engineering

Mathematics

Tangent to Ellipse

Question

If the tangents on the ellipse 4x² + y² = 8 at the points (1, 2) and (a, b) are perpendicular to each other, then a² is equal to

$\frac{2}{17}$

$\frac{4}{17}$

$\frac{128}{17}$

$\frac{64}{17}$

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4a² + b² = 8 …………..(1)

${\frac{dy}{dx})}_{(1, 2)} = - \frac{4 x}{y} = - 2$

$\Rightarrow - \frac{4 a}{b} = \frac{1}{2}$

B = –8a

⇒ b² = 64a²

68a² = 8, a² $= \frac{2}{17}$