If A1B1 and A2B2 are two focal chords of...

If `A_1B_1` and `A_2B_2` are two focal chords of the parabola `y^2=4a x ,` then the chords `A_1A_2` and `B_1B_2` intersect on

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If t_1a n dt_2 are the ends of a focal chord of the parabola y^2=4a x , then prove that the roots of the equation t_1x^2+a x+t_2=0 are real.

If (2,-8) is at an end of a focal chord of the parabola y^2=32 x , then find the other end of the chord.

The focal chord of the parabola y^2=a x is 2x-y-8=0 . Then find the equation of the directrix.

The locus of the middle points of the focal chords of the parabola, y^2=4x is:

If (at^(2) , 2at) be the coordinate of an extremity of a focal chord of the parabola y^(2) =4ax, then the length of the chord is-

If a and c are the lengths of segments of any focal chord of the parabola y^2=2b x ,(b >0), then the roots of the equation a x^2+b x+c=0 are (a) real and distinct (b) real and equal (c) imaginary (d) none of these

Let A(x_(1),y_(1)) and B(x_(2),y_(2)) be two points on the parabola y^(2) = 4ax . If the circle with chord AB as a dimater touches the parabola, then |y_(1)-y_(2)| is equal to

If (at^(2) , 2at ) be the coordinates of an extremity of a focal chord of the parabola y^(2) = 4ax , then show that the length of the chord is a(t+(1)/(t))^(2) .

If the length of a focal chord of the parabola y^2=4a x at a distance b from the vertex is c , then prove that b^2c=4a^3 .

If athe coordinates of one end of a focal chord of the parabola y^(2) = 4ax be (at^(2) ,2at) , show that the coordinates of the other end point are ((a)/(t^(2)),(2a)/(t)) and the length of the chord is a(t+(1)/(t))^(2)

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions

If the tangents and normal at the extremities of focal chord of a para...
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Radius of the circle that passes through the origin and touches the ...
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If A1B1 and A2B2 are two focal chords of the parabola y^2=4a x , then ...
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y=x+2 is any tangent to the parabola y^(2)=8x. The point P on this tan...
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Two parabola have the same focus. If their directrices are the x-and t...
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The triangle P Q R of area A is inscribed in the parabola y^2=4a x suc...
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The length of the chord of the parabola y^(2)=x which is bisected at t...
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The circle x^2+y^2=5 meets the parabola y^2=4x at P and Q . Then the l...
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A line is drawn form A(-2,0) to intersect the curve y^2=4x at Pa n dQ ...
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Let y=f(x) be a parabola, having its axis parallel to the y-axis, whic...
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Two mutually perpendicular tangents of the parabola y^(2)=4ax meet the...
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Let S be the focus of y^2=4x and a point P be moving on the curve s...
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If a!=0 and the line 2b x+3c y+4d=0 passes through the points of ...
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If y(1),y(2),andy(3) are the ordinates of the vertices of a triangle i...
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The circle x^(2)+y^(2)+2lamdax=0,lamdainR, touches the parabola y^(2)=...
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If P S Q is a focal chord of the parabola y^2=8x such that S P=6 , the...
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Parabolas y^(2)=4a(x-c(1))andx^(2)=4a(y-c(2)), where c(1) and c(2) are...
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A circle touches the x-axis and also touches the circle with centre (0...
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The locus of the vertex of the family of parabolas y=(a^(3)x^(2))/(3...
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Let C(1)andC(2) be, respectively, the parabola x^(2)=y-1andy^(2)=x-1. ...
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