Question:
The vertices of a hyperbola $H$ are $(\pm 6,0)$ and its eccentricity is $\frac{\sqrt{5}}{2}$ Let $N$ be the normal to $H$ at a point in the first quadrant and parallel to the line $\sqrt{2} x+y=2 \sqrt{2}$If $d$ is the length of the line segment of $N$ between $H$ and the $y$-axis then $d^2$ is equal to
The vertices of a hyperbola $H$ are $(\pm 6,0)$ and its eccentricity is $\frac{\sqrt{5}}{2}$ Let $N$ be the normal to $H$ at a point in the first quadrant and parallel to the line $\sqrt{2} x+y=2 \sqrt{2}$If $d$ is the length of the line segment of $N$ between $H$ and the $y$-axis then $d^2$ is equal to
Updated On: Sep 30, 2024
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Correct Answer: 216
Solution and Explanation
The correct answer is 216.
equation of normal is
Equation of normal is
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Concepts Used:
Hyperbola
Hyperbola is the locus of all the points in a plane such that the difference in their distances from two fixed points in the plane is constant.
Hyperbola is made up of two similar curves that resemble a parabola. Hyperbola has two fixed points which can be shown in the picture, are known as foci or focus. When we join the foci or focus using a line segment then its midpoint gives us centre. Hence, this line segment is known as the transverse axis.
