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The tangent at the point P(x1, y1) to th...

The tangent at the point `P(x_1, y_1)` to the parabola `y^2 = 4 a x` meets the parabola `y^2 = 4 a (x + b)` at Q and R. the coordinates of the mid-point of QR are

A

`(x_(1)+b,y_(1)+b)`

B

`(x_(1)-b,y_(1)-b)`

C

`(x_(1),y_(1))`

D

`(x_(1)+b,y_(1))`

Text Solution

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The correct Answer is:
C
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MOTION-PARABOLA-EXERCISE - I
  1. If (t^2, 2t) is one end ofa focal chord of the parabola, y^2=4x then ...

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  2. Find the locus of the point of intersection of the perpendicular ta...

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  3. Find the common tangent of x^(2) + y^(2) = 2a^(2) and y^(2) = 8ax.

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  4. The tangents to the parabola x = y^2 + c from origin are perpendicular...

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  5. T P and T Q are tangents to the parabola y^2=4a x at Pa n dQ , respect...

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  6. P Q is a normal chord of the parabola y^2=4a x at P ,A being the verte...

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  7. The normal at the point (bt1^2, 2bt1) on the parabola y^2 = 4bx meets ...

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  8. Locus of the intersection of the tangents at the ends of the normal ch...

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  9. If the normal chhord of the parabola y^(2)=4x makes an angle 45^(@) wi...

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  10. If x+y=k is normal to y^2=12 x , then k is 3 (b) 9 (c) -9 (d) -3

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  11. Tangents are drawn from the points on the line x-y+3=0 parabola y^2=8x...

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  12. The line 4x-7y + 10 = 0 intersects the parabola, y^2 = 4x at the point...

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  13. From the point (4, 6) a pair of tangent lines are drawn to the parabol...

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  14. PSQ is a focal chord of the parabola y^2=8xdotIf\ S P=6, then write SQ...

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  15. The equation of the circle drawn with the focus of the parabola (x – 1...

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  16. The slope of the focal chords of the parabola y^(2) = 16x which are ta...

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  17. The equation of the common tangent touching the circle (x-3)^2+y^2=9 a...

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  18. AB, AC are tangents to a parabola y^2=4ax; p1, p2, p3 are the lengths...

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  19. A point on the parabola y^2=18 x at which the ordinate increases at tw...

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  20. The tangent at the point P(x1, y1) to the parabola y^2 = 4 a x meets t...

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