MCA Entrance Previous Year Question Bank

A general second--degree equation of a conic is $a{x}^2+2hxy+b{y}^2+2gx+2fy+c=0$, where $a,b,c,f,g,$ and $h$ are constants.

Which of the following statements are true?

(A) The given conic is a circle if $a=0$ and $b=0$

(B) The given conic is a circle if $a=b\ne 0$ and $h=0$

(C) The given conic is a circle if $a=b\ne 0$ and $h\ne 0$

(D) The given conic represents a pair of real and distinct straight lines if $f=g=c=0$ and h^{2} - ab > 0

Choose the correct answer from the options given below.

Match List-I with List-II

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The center and radius for the circle $$x^2+y^2+6x-4y+4=0$$ respectively are:

If x² = -16y is an equation of parabala then:

(A) directrix is y = 4

(B) directrix is x = 4

(C) co-ordinates of focus are (0,-4)

(D) co-ordinates of focus are (-4,-0)

(E) length of latusrectum = 16

Choose the correct answer from the options given below:

The length of major axis and coordinate of vertices for the ellipse $3x^2+2y^2=6$ respectively are: