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AMU MCA Previous Year Questions (PYQs)

AMU MCA Parabola PYQ

AMU MCA PYQ
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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AMU MCA Previous Year PYQ AMU MCA AMU MCA 2022 PYQ

Solution

AMU MCA PYQ
The tangents at the extremities of a focal chord of a parabola intersect on the directrix at an angle





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AMU MCA Previous Year PYQ AMU MCA AMU MCA 2022 PYQ

Solution

AMU MCA PYQ
The locus of points from which three mutually perpendicular tangents can be drawn to $ ax^2+by^2=2z $ is





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AMU MCA Previous Year PYQ AMU MCA AMU MCA 2021 PYQ

Solution

Standard result for paraboloid: $ a(x^2+y^2)-(a+b)z=1 $
AMU MCA PYQ
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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AMU MCA Previous Year PYQ AMU MCA AMU MCA 2020 PYQ

Solution

For perpendicular focal chords of parabola, required sum = $\frac{1}{4}$


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