The coordinates of a moving point P are (2t2 + 4, 4t + 6). Then, its locus will be
circle
straight line
parabola
ellipse
C.
parabola
Let x = 2t2 + 4, y = 4t + 6
hence, it is a locus of a parabola.
The equation 8x2 + 12y2 - 4x + 4y - 1 = 0 represents
an ellipse
a hyperbola
a parabola
a circle
If the straight line y = mx lies outside the circle x2 + y2 - 20y + 90 = 0, then the value of m will satisfy
m < 3
m > 3
The locus of the passes through (a, 0), (- a, 0) is the centre of a circle which two variable points
x = 1
x + y = a
x + y = 2a
x = 0
The intercept on the line y = x by the circle x2 = y2 - 2x = 0 is AB. Equation of the circle with AB as the diameter is
x2 + y2 = 1
x(x - 1) + y(y - 1) = 0
x2 + y2 = 2
(x - 1)(x - 2) + (y - 1)(y - 2) = 0
If the coordinates of one end of a diameter of the circle x2 + y2 + 4x-8y + 5 = 0 are (2, 1), the coordinates of the other end are
(- 6, - 7)
(6 , 7)
(- 6, 7)
(7, - 6)
The locus of the middle points of all chords of the parabola y2 = 4ax passing through the vertex is
a straight line
an ellipse
a parabola
a circle
Prove that the centre of the smallest circle passing through origin and whose centre lies on y = x + 1 is
If t1 and t2 be the parameters of the end points of a focal chord for the parabola y2 = 4ax, then which one is true?
t1t2 = 1
t1t2 = - 1
t1 + t2 = - 1
S and T are the foci of an ellipse and B is end point of the minor axis. If STB is an equilateral triangle, the eccentricity of the ellipse is