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P, Q, and R are the feet of the normals ...

P, Q, and R are the feet of the normals drawn to a parabola (`y−3)^2=8(x−2)`. A circle cuts the above parabola at points P, Q, R, and S. Then this circle always passes through the point. (a)(2, 3)(b)(3, 2)(c)(0, 3) (d) (2, 0 )

A

(2,3)

B

(3,2)

C

(0,3)

D

(2,0)

Text Solution

Verified by Experts

The correct Answer is:
A
(1) A circle through three co-normal point of a parabola always passes through the vertex of the parabola. Hence, the circle through P,Q,R and S out of which P,Q and R are co-normals points will always pass through vertex (2,3) of the parabola.
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CENGAGE-PARABOLA-Exercise (Single)
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  2. If the normals to the parabola y^2=4a x at three points (a p^2,2a p), ...

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  3. Normals A O ,AA1a n dAA2 are drawn to the parabola y^2=8x from the poi...

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

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  5. From a point (sintheta,costheta), if three normals can be drawn tot he...

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

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

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

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

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

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

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

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

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

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  15. From the point (15, 12), three normals are drawn to the parabola y^2=4...

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

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  17. If normal are drawn from a point P(h , k) to the parabola y^2=4a x , t...

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  18. The circle x^2+y^2+2lambdax=0,lambda in R , touches the parabola y^2=...

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  19. The radius of the circle whose centre is (-4,0) and which cuts the par...

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

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