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The equation of the common tangent to th...

The equation of the common tangent to the parabolas `y^2= 4ax` and `x^2= 4by` is given by

A

3

B

4

C

6

D

5

Text Solution

Verified by Experts

The correct Answer is:
D
(4) Normal to `y^(2)=4axandx^(2)=4by` in terms of m are
`y=mx-2am-am^(3)`
`andy=mx+2b+(b)/(m^(2))`
For a common normal,
`2b+(b)/(m^(2))+2am+am^(3)=0`
`oram^(5)+2am^(3)+2bm^(2)+b=0`
This means there can be at most five common normals
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CENGAGE PUBLICATION-PARABOLA-EXERCISE (SINGLE CORRECT ANSWER TYPE )
  1. The radius of the circle touching the parabola y^2=x at (1, 1) and hav...

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  2. If two different tangents of y^2=4x are the normals to x^2=4b y , then

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  3. The equation of the common tangent to the parabolas y^2= 4ax and x^2=...

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  4. If line P Q , where equation is y=2x+k , is a normal to the parabola w...

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  5. Evaluate, min[(x1-x2)^2+(5+sqrt(1-x1^2)-sqrt(4x2))^2],AAx1,x2 in R , ...

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  6. If the normals to the parabola y^2=4a x at three points (a p^2,2a p), ...

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  7. Normals A O ,A A1a n dA A2 are drawn to the parabola y^2=8x from the p...

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  8. If the normals to the parabola y^2=4a x at the ends of the latus rectu...

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  9. From a point (sintheta,costheta), if three normals can be drawn to the...

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  10. If the normals at P(t(1))andQ(t(2)) on the parabola meet on the same p...

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  11. If the normals to the parabola y^2=4a x at P meets the curve again at ...

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  12. PQ is a normal chord of the parabola y^2 =4ax at P, A being t...

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  13. P ,Q , and R are the feet of the normals drawn to a parabola (y-3)^2=8...

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  14. Normals at two points (x1y1)a n d(x2, y2) of the parabola y^2=4x meet ...

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  15. The endpoints of two normal chords of a parabola are concyclic. Then ...

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  16. If normal at point P on the parabola y^2=4a x ,(a >0), meets it again ...

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  17. The set of points on the axis of the parabola (x-1)^(2)=8(y+2) from wh...

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  18. Tangent and normal are drawn at the point P-=(16 ,16) of the parabola ...

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  19. In parabola y^2=4x, From the point (15,12), three normals are drawn th...

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  20. The line x-y=1 intersects the parabola y^2=4x at A and B . Normals at ...

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