JEE Main 2022 · 25 Jul · Shift 1 · Mathematics Q29

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MathematicsInteger+4 / -1Question 29 of 90

The sum of diameters of the circles that touch (i) the parabola $75x^2=64(5y-3)$ at the point $\left(\dfrac85,\dfrac65\right)$ and (ii) the $y$ -axis, is equal to ______.

Your answer

Answer and worked solution

Official answer: 10

Normal at $\left(\frac85,\frac65\right)$ has slope $-\frac43$ . Centres on it with radius equal to $|x|$ give radii 1 and 4.

Diameters $2+8=10$ .

Answer: 10

Topics:Parabola Tangents and normals

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JEE Main 2022 · 25 Jul · Shift 1, Mathematics question 29