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Byju's Answer

Standard XII

Mathematics

Perpendicular Distance of a Point from a Line

Suppose OAB...

Question

Suppose $O A B C$ is a rectangle in the $x y - p l a n e$ where $o$ is the origin and $A, B$ lie on the parabola $y = x^{2}$ . Then $C$ must lie on the curve.

y = x^{2} + 2

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y = 2 x^{2} + 1

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y = - x^{2} + 2

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y = - 2 x^{2} + 1

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Solution

The correct option is A $y = x^{2} + 2$
$m_{O A} \times m_{O B} = - 1$
$t_{1} t_{2} = - 1$
$t_{1} + t_{2} = h$
$K = (t_{1} + t_{2})^{2} - 2 t_{1} t_{2}$
$K = h^{2} + 2 \Rightarrow y = x^{2} + 2$ .

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Similar questions

Q. Suppose

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Suppose OABC is a rectangle in the xy−plane where o is the origin and A,B lie on the parabola y=x2. Then C must lie on the curve.

The correct option is A y=x2+2mOA×mOB=−1t1t2=−1t1+t2=hK=(t1+t2)2−2t1t2K=h2+2⇒y=x2+2.

Suppose $O A B C$ is a rectangle in the $x y - p l a n e$ where $o$ is the origin and $A, B$ lie on the parabola $y = x^{2}$ . Then $C$ must lie on the curve.

The correct option is A $y = x^{2} + 2$
$m_{O A} \times m_{O B} = - 1$
$t_{1} t_{2} = - 1$
$t_{1} + t_{2} = h$
$K = (t_{1} + t_{2})^{2} - 2 t_{1} t_{2}$
$K = h^{2} + 2 \Rightarrow y = x^{2} + 2$ .