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Byju's Answer

Standard XII

Mathematics

Intercept Made by Circle on Axes

A tangent to ...

Question

A tangent to the hyperbola $\frac{x^{2}}{4} - \frac{y^{2}}{2} = 1$ meets x-axis at P and y-axis at Q. Lines PR and QR are drawn such that OPRQ is a rectangle (where O is the origin) then R lies on:

\frac{4}{x^{2}} + \frac{2}{y^{2}} = 1

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\frac{2}{x^{2}} - \frac{4}{y^{2}} = 1

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

\frac{2}{x^{2}} + \frac{4}{y^{2}} = 1

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

\frac{4}{x^{2}} - \frac{2}{y^{2}} = 1

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Solution

The correct option is D $\frac{4}{x^{2}} - \frac{2}{y^{2}} = 1$
The answer
$3$ lies on $\frac{4}{x^{2}} - \frac{2}{y^{2}} = 1$
Option $D$ is correct

Suggest Corrections

Similar questions

Q. A tangent to the hyperbola

x^{2} - 2 y^{2} = 4

meets x-axis at P and Y-axis at 'Q'. Line PR and QR are drawn such that OPRQ is a rectangle (where O is origin). The locus of R is:

Q. From the point

P (1, \sqrt{3})

on the circle

x^{2} + y^{2} =

a tangent is drawn to the hyperbola

\frac{x^{2}}{4} - \frac{y^{2}}{1} = 1

which meets its transverse axis at

Q

. From

Q

a line is drawn parallel to conjugate axis, which cuts the hyperbola at

R

above the x-axis, then

P R

equals.

Q. Let

P

be a point on the ellipse

\frac{x^{2}}{9} + \frac{y^{2}}{4} = 1

and the line through

P

parallel to the y-axis meets the circle

x^{2} + y^{2} = 9

Q

, where

P, Q

are on the same side of the x-axis. If

T

is a point on

P Q

such that

\frac{P R}{P Q} = \frac{1}{2}

, then the locus of

R

is:

Q. Two tangents are drawn from a point on hyperbola

x^{2} - y^{2} = 5

to the ellipse

\frac{x^{2}}{9} + \frac{y^{2}}{4} = 1

. If they make angle

α

and

β

with x-axis then:

Q. If

z = x + i y

and

| z - 1 |^{2} + | z + 1 |^{2} = 4

, then the locus of

z

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A tangent to the hyperbola x24−y22=1 meets x-axis at P and y-axis at Q. Lines PR and QR are drawn such that OPRQ is a rectangle (where O is the origin) then R lies on:

The correct option is D 4x2−2y2=1The answer3 lies on 4x2−2y2=1Option D is correct

A tangent to the hyperbola $\frac{x^{2}}{4} - \frac{y^{2}}{2} = 1$ meets x-axis at P and y-axis at Q. Lines PR and QR are drawn such that OPRQ is a rectangle (where O is the origin) then R lies on:

The correct option is D $\frac{4}{x^{2}} - \frac{2}{y^{2}} = 1$
The answer
$3$ lies on $\frac{4}{x^{2}} - \frac{2}{y^{2}} = 1$
Option $D$ is correct