CameraIcon

SearchIcon

MyQuestionIcon

1

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

Length of Common Chord

l and m are...

Question

$l$ and $m$ are the lengths of the tangents from the origin and the point $(9, - 1)$ to the circle $x^{2} + y^{2} + 18 x - 2 y + 32 = 0$ . The value of $17 (l^{2} + m^{2})$ is equal to

Open in App

Solution

Given equation of circle is
$x^{2} + y^{2} + 18 x - 2 y + 32 = 0$
Square of length of tangent from (0,0) is
$l^{2} = 32$
Square of length of tangent from (9,-1) is
$m^{2} = 81 + 1 + 162 + 2 + 32 = 278$
So, $17 (l^{2} + m^{2}) = 17 (310) = 5270$

Suggest Corrections

thumbs-up

0

Similar questions

Q. The point, the length of the tangents from which to the following three circles

x^{2} + y^{2} + 4 x + 6 y - 19 = 0

x^{2} + y^{2} - 2 x - 2 y - 5 = 0

x^{2} + y^{2} - 9 = 0

Q. Tangents are drawn from the point

P (2, 2)

x^{2} + y^{2} = 1,

touching the circle at

A

B .

Then equation of circumcircle of

△ P A B

Q. If the length of the tangents from

(a, b)

x^{2} + y^{2} - 4 x - 5 = 0

x^{2} + y^{2} + 6 x - 2 y + 6 = 0

are equal, then the value of

10 a - 2 b

Q. If the lengths of the tangents from a point to the circles

S_{1} : x^{2} + y^{2} - 16 x + 60 = 0,

S_{2} : x^{2} + y^{2} - 12 x + 20 = 0,

S_{3} : x^{2} + y^{2} - 16 x - 12 y = 0

, are equal and its value is

L

L

.

Q. The point from which the lengths of tangents to the three circles

x^{2} + y^{2} - 4 = 0, x^{2} + y^{2}

+ 3 y = 0

x^{2} + y^{2} + 7 y - 18 = 0

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Length of Common Chord

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon