MyQuestionIcon

1

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

Length of Intercept Made by a Circle on a Straight Line

Let L1 be a s...

Question

Let $L_{1}$ be a straight line passing through the origin and $L_{2}$ be the straight line x + y = 1. If the intercepts made by

the circle $x^{2} + y^{2} - x + 3 y = 0$ on $L_{1}$ and $L_{2}$ are equal, then which of the following equations can represent $L_{1}$

A

x + y = 0

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

B

x - y = 0

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

C

x + 7y = 0

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

D

x - 7y = 0

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

Open in App

Solution

The correct option is B
x - y = 0

$x + y = 1, x^{2} + y^{2} - x + 3 y = 0 x^{2} + (1 - x)^{2} - x + 3 (1 - x) = 0 x^{2} + 1 + x^{2} - 2 x - x + 3 - 3 x = 0 2 x^{2} - 6 x + 4 = 0 x^{2} - 3 x + 2 = 0 x = 1, 2 A (1, 0), B (2, - 1) A B = \sqrt{1 + 1} = \sqrt{2} ∴ y = x 2 x^{2} + 2 x = 0 x = 0, - 1 y = x (0, 0), (- 1, - 1) \sqrt{1 + 1} = \sqrt{2}$

Suggest Corrections

thumbs-up

0

Similar questions

L_{1}

be a tangent to the parabola

y^{2} = 4 (x + 1)

L_{2}

be a tangent to the parabola

y^{2} = 8 (x + 2)

L_{1}

L_{2}

intersect at right angles. Then

L_{1}

L_{2}

meet on the straight line:

L_{1} : \frac{x - 1}{2} = \frac{y - 2}{1} = \frac{z - 3}{1}

L_{2} : \frac{x}{1} = \frac{y}{- 1} = \frac{z - 5}{3}

The equation of the line perpendicular to

L_{1}

L_{2}

and passing through the point of intersection of

L_{1}

L_{2}

l_{1}

\frac{x}{5 / 3} + \frac{y}{5 / 4} = 1

l_{2}

be perpendicular to it. If

l_{1}

x -

intercept equals to

2

l_{2}

y -

intercept equals to

2

units, then the absolute value of the ratio of

y -

l_{1}

x -

l_{2}

Q. A straight line

L_{1} : x - 2 y + 10 = 0

meets the circle with equation

x^{2} + y^{2} = 100

B

in the first quadrant. If another line

L_{2}

B

is perpendicular to

L_{1}

y

P (0, t)

, then the value of

t

L_{1}

\frac{x}{5} + \frac{y}{b} = 1

passes through the point

M (13, 32)

L_{2}

L_{1}

and has the equation

\frac{x}{c} + \frac{y}{3} = 1

. Then the distance between

L_{1}

L_{2}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Length of Intercept Made by a Circle on a Straight Line

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon