You visited us 1 times! Enjoying our articles? Unlock Full Access!

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

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

y = 2 x^{2} + 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

y = - x^{2} + 2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

y = - 2 x^{2} + 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

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

Suggest Corrections

Similar questions

Q. Suppose

O A B C

is a rectangle in the

x y -

plane where

O

is the origin and

A, B

lie on the parabola

y = x^{2}

. Then

C

must lie on the curve

Q. Let

O A B C

be a rectangle, where

O

is the origin and

A

C

lie on the parabola

y = x^{2}

. If

B

lies on a parabola whose vertex coordinates is

(α, β)

, then the value of

α + β

Q. Let

O A B C

be a rectangle, where

O

is the origin and

A

C

lie on the parabola

y = x^{2}

. If

B

lies on a parabola whose vertex coordinates is

(α, β)

, then the value of

α + β

Q. The above figure shows rectangle

A B C D

. Points A and D are on the parabola

y = 2 x^{2} - 8

, and points B and C are on the parabola

y = 9 - x^{2}

. Calculate the area of rectangle

A B C D

if point B has coordinates

(- 1.50, 6.75)

Q. Let

τ

denote a curve

y = y (x)

which is in the first quadrant and let the point

(1, 0)

lie on it. Let the tangent to

τ

at a point

P

intersect the y-axis at

Y_{p}

. If

P Y_{p}

has length

1

for each point

P

τ

, then which of the following options is /are correct?

Join BYJU'S Learning Program

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