The area included between the parabolas y2 = 4x and x2 = 4y is
sq unit
8 sq unit
sq unit
12 sq unit
The locus of the centres of the circles which touch both the axes is given by
x2 - y2 = 0
x2 + y2 = 0
x2 - y2 = 1
x2 + y2 = 1
The latusrectum of an ellipse is equal to one-half of its minor axis. The eccentricity of the ellipse is
Prove that for all values of m, except zero the straight line
y = mx + touches the parabola y2 = 4ax.
If the lines 3x - 4y - 7 = 0 and 2x - 3y - 5 = 0 are two diameters of a circle of area 49 sq unit, then equation of the circle is
x2 + y2 + 2x - 2y - 62 = 0
x2 + y2 - 2x + 2y - 62 = 0
x2 + y2 - 2x + 2y - 47 = 0
x2 + y2 + 2x - 2y - 47 = 0
The locus of middle point of chords of hyperbola 3x2 - 2y2 + 4x - 6y = 0 parallel to y = 2x is
3x - 4y = 4
3x - 4x + 4 = 0
4x - 3y = 3
3x - 4y = 2
The equation of the common tangent touching the circle (x - 3)2 + y2 = 9 and parabola y = 4x above the x-axis is
√3y = 3x + 1
√3y = -( x + 3 )
√3y = x + 3
√3y = -( 3x + 1 )
The equation of the tangents to the ellipse 4x2 + 3y2 = 5 which are parallel to the line y = 3x + 7 are
None of these
B.
Given, equation of ellipse is 4x2 + 3y2 = 5
Here,
Given, line y = 3x + 7, It's slope is 3, therefore slope of the parallel line is also 3.
Now, equations of tangent are,
The radius of the circle passing through the foci of the ellipse and having its centre (0, 3) is
4
3
7/2
The equation of the circle on the common chord of the circles (x - a)2 + y2 = a2 and x2 + (y + b)2 = b2 as diameter is
x2 + y2 = 2ab(bx + ay)
x2 + y2 = bx + ay
(a2 + b2)(x2 + y2) = 2ab(bx - ay)
(a2 + b2)(x2 + y2) = 2(bx + ay)