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QJEEM19Ma6a65: JEE Main 2019 Mathematics - Class 11 JEEM19Ma6a65 Solution: If a circle of radius R passes through the origin O and…

If a circle of radius R passes through the origin O and intersects the coordinates axes at A and B, then the locus of the foot of perpendicular from O on AB is :

Multiple Choice Options

  • A (x2 + y2)2 = 4R2x2y2
  • B (x2 + y2) (x + y) = R2xy
  • C (x2 + y2)2 = 4Rx2y2
  • D (x2 + y2)3 = 4R2x2y2

Step-by-Step Verified Solution

JEE Main 2019 (Online) 12th January Evening Slot Mathematics - Circle Question 118 English Explanation
Slope of AB = −hk{{ - h} \over k}

Equation of AB is hx + ky = h2 + k2

A (h2+k2h,0),B(0,h2+k2k)\left( {{{{h^2} + {k^2}} \over h},0} \right),B\left( {0,{{{h^2} + {k^2}} \over k}} \right)

AB = 2R

⇒\Rightarrow    (h2 + k2)3 = 4R2h2k2

⇒\Rightarrow   (x2 + y2)3 = 4R2x2y2

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