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The equation of the tangent to the circl...

The equation of the tangent to the circle `x^2+y^2=25` passing through `(-2,11)` is (a) `4x+3y=25` (b) `3x+4y=38` (c) `24 x-7y+125=0` (d) `7x+24 y=250`

A

`4x+3y=25`

B

`3x+4y=38`

C

`24x-7y+125=0`

D

`7x+24y=250`

Text Solution

Verified by Experts

The correct Answer is:
1,3
The equation of any tangent to the circle `x^(2)+y^(2)=25` is of form
`y= mx + 5 sqrt(1+m^(2))` (where m is the slope )
It passes through `( -2,11) ` .Therefore,
`11= - 2m +5 sqrt(1+m^(2))`
or `(11+2m)^(2) = 25 (1+m^(2))`
or `m=(24)/(7),- (4)/(3)`
Thereforem the equation of tangent is
`24x-7y+125=0`
or `4x+3y=25`
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