AMU MCA Parabola Previous Year Questions (PYQs)
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Showing 7 questions
The normal to the parabola $y^2 = 8x$ at the point $(2,4)$ meets the parabola again at the point
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In what direction is the derivative of $f(x,y)=x^2-xy+y^2$ at $P(1,-1)$ equal to zero?
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The tangents at the extremities of a focal chord of a parabola intersect on the directrix at an angle
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The shortest distance between the parabolas
$ 2y^2 = 2x - 1 $, $ 2x^2 = 2y - 1 $ is
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The directrix of the parabola $4y^2 + 12x - 12y + 39 = 0$ is
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$4(y^2 - 3y) + 12x + 39 = 0$
$4[(y - \frac{3}{2})^2 - \frac{9}{4}] + 12x + 39 = 0$
$4(y - \frac{3}{2})^2 + 12x + 30 = 0$
$(y - \frac{3}{2})^2 = -3(x + \frac{5}{2})$
Here $a = -\frac{3}{4}$
Directrix: $x = -\frac{5}{2} - a = -\frac{5}{2} + \frac{3}{4} = -\frac{7}{4}$
Final Answer: $\boxed{x = -\frac{7}{4}}$
The locus of points from which three mutually perpendicular tangents can be drawn to
$ ax^2+by^2=2z $
is
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Solution
Standard result for paraboloid:
$ a(x^2+y^2)-(a+b)z=1 $
If PSP' and QSQ' be two perpendicular focal chords of parabola $y^2 = 4x$, then $\frac{1}{SP \cdot SP'} + \frac{1}{SQ \cdot SQ'}$ equals
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Solution
For perpendicular focal chords of parabola, required sum = $\frac{1}{4}$
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