The line x - 1 = 0 is the directrix of the parabola y2 - kx + 8 = 0. Then, one of the value of k is
8
4
If 5x - 12y + 10 = 0 and 12y - 5x + 16 = 0 are two tangents to a circle, then the radius of the circle is
1
2
4
6
The area of the smaller segment cut off from the circle x2 + y2 = 9 by x = 1 is
sq unit
None of the above
An equilateral triangle is inscribed in the parabola y2 = 4ax, whose vertex is at the vertex of the parabola. The length of its side is
2a
4a
8a
The foci of a hyperbola are (- 5, 18) and (10, 20) and it touches the Y-axis. The length of its transverse axis is
100
The locus of mid-point of the line segment joining the locus to a moving point on the parabola y2 = 4ax is another parabola with directrix
x = - a
x = a
x = 0
x = a/2
The equation of the ellipse with its centre at (1, 2), one locus at (6, 2) and passing through (4, 6) is
None of the above
A.
Let the equation of the ellipse be,
It passes through ( 4, 6)
Let e be the eccentricity of the ellipse. Then, ae = Distance between (1, 2) and (6, 2)
Solving (ii) and (iii), we get
a2 = 45 and b2 = 20
Hence, the equation of the ellipse is,