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The lines y = 2x + sqrt 76 and 2y + x=8 ...

The lines `y = 2x + sqrt 76 and 2y + x=8 `touch the ellipse `(x ^(2))/(16 )+(y ^(2))/(12)=1.`If the point of intersection of these two lines lie on a circle, whose centre coincides with the centre of that ellipse, then the equation of that circle is

A

`x ^(2) + y^(2) =16`

B

`x ^(2) + y^(2)=12`

C

`x ^(2) + y^(2)=28`

D

`x ^(2) + y^(2) =(4+sqrt8)^(2)`

Text Solution

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The correct Answer is:
C
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TARGET PUBLICATION-CIRCLE AND CONICS -COMPETITIVE THINKING
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  2. If the foci of the ellipse (x^(2))/(16)+(y^(2))/(b^(2))=1 and the hype...

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  3. Let the eccentricity of the hyperbola (x ^(2))/(a ^(2))- (y ^(3))/(b ^...

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  4. Let the eccentricity of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=...

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  5. The length of the straight line x-3y=1, intercept by the hyperbola x^2...

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  6. The locue of the mis-points of the chords of the circel x ^(2) + y ^(2...

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  7. If x + y+ k =0 touches the circle x ^(2) + y^(2) -2x -4y + 3 =0, then ...

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  8. If the lines 3x-4y+4=0a d n6x-8y-7=0 are tangents to a circle, then fi...

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  9. From the point A(0,3) on the circle x^2 +4x + (y-3)^2 = 0 a chord AB ...

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  10. For any a in R, then locus x ^(2) + y^(2) - 2ay + a ^(2) =0 touches ...

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  11. The equation of a diameter of circle x ^(2) + y^(2)-6x + 2y =0, passin...

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  12. The centres of those circles which touch the circle x^(2) + y^(2) - 8...

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  13. Let A be the centre of the circle x^(2)+y^(2)-2x-4y-20=0 .The tangents...

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  14. Let the orthocentre and centroid of a triangle be (-3,5) and B(3,3) r...

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  15. The equation of a parabola which passes through the point of intersect...

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  16. Let the equation of an ellipse be (x^(2))/(144) + (y^(2))/(25) = 1 ....

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  17. The lines y = 2x + sqrt 76 and 2y + x=8 touch the ellipse (x ^(2))/(16...

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  18. A bar of given length moves with its extremities on two fixed strai...

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  19. The distance of the mid -point of line joining two ponts (4,0) and (0,...

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  20. Tangents are drawn to the hyperbola 4x^2-y^2=36 at the points P and Q....

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