jee-main 2014 Q71

jee-main · India · 09apr Circles Circle-Related Locus Problems

Let $a$ and $b$ be any two numbers satisfying $\frac { 1 } { a ^ { 2 } } + \frac { 1 } { b ^ { 2 } } = \frac { 1 } { 4 }$. Then, the foot of perpendicular from the origin on the variable line $\frac { x } { a } + \frac { y } { b } = 1$ lies on:
(1) A circle of radius $= 2$
(2) A hyperbola with each semi-axis $= \sqrt { 2 }$.
(3) A hyperbola with each semi-axis $= 2$
(4) A circle of radius $= \sqrt { 2 }$

Let $a$ and $b$ be any two numbers satisfying $\frac { 1 } { a ^ { 2 } } + \frac { 1 } { b ^ { 2 } } = \frac { 1 } { 4 }$. Then, the foot of perpendicular from the origin on the variable line $\frac { x } { a } + \frac { y } { b } = 1$ lies on:\\
(1) A circle of radius $= 2$\\
(2) A hyperbola with each semi-axis $= \sqrt { 2 }$.\\
(3) A hyperbola with each semi-axis $= 2$\\
(4) A circle of radius $= \sqrt { 2 }$

Paper Questions

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