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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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CENGAGE-CIRCLE -Exercise (Multiple)
  1. If the circle x^2+y^2=a^2 intersects the hyperbola x y=c^2 at four poi...

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  4. A point on the line x=3 from which the tangents drawn to the circle x^...

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  6. If the circles x^2+y^2-9=0 and x^2+y^2+2a x+2y+1=0 touch each other, t...

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  8. The equation of the tangent to the circle x^2+y^2=25 passing through (...

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  9. If the area of the quadrilateral by the tangents from the origin to th...

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  10. The equation of the circle which touches the axes of coordinates and ...

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  11. Which of the following lines have the intercepts of equal lengths on t...

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  12. The equation of the line(s) parallel to x-2y=1 which touch(es) the cir...

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  13. The circles x^2+y^2-2x-4y+1=0 and x^2+y^2+4x+4y-1=0 (a)touch internal...

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  16. The equation of a circle of radius 1 touching the circles x^2+y^2-2|x|...

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  17. The center(s) of the circle(s) passing through the points (0, 0) and ...

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  18. Find the equations of straight lines which pass through the intersecti...

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  19. Two lines through (2, 3) from which the circle x^2+y^2 =25 intercepts ...

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  20. Normal to the circle x^(2)+y^(2)=4 divides the circle having centre at...

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