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Prove that the locus of the point of int...

Prove that the locus of the point of intersection of the normals at the ends of a system of parallel chords of a parabola is a straight line which is a normal to the curve.

A

`2 xm^2-ym^3= 4a(2+m^2)`

B

`2 xm^2+ym^3= 4a(2+m^2)`

C

`2 xm+ym^2= 4a(2+m^2)`

D

`2 xm^2-ym^3= 4a(2-m^2)`

Text Solution

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The correct Answer is:
A
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VMC MODULES ENGLISH-CONIC SECTIONS-LEVEL - 1
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  2. If (-2a,a+1) lies in the interior (smaller region) bounded by the circ...

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  9. The maximum number of common chords of a parabola and a circle can be

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  10. If a!=0 and the line 2b x+3c y+4d=0 passes through the points of in...

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  11. If length of focal chord P Q is l , and p is the perpendicular distanc...

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

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  14. The mid-point of the chord intercepted on the line 4x-3y+4=0 by the pa...

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  15. The polar of a point with respect to y^2=4x touches x^2=4y. If the loc...

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  16. Let A and B be two points on y^(2)=4ax such that normals to the curve ...

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

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  18. If the circle x ^(2) + y^(2) + 2gx + 2fy+ c=0 touches X-axis, then

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  19. Find the minimum distance between the curves y^(2)=4x and x^(2)+y^(2)-...

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