The locus of the foot of perpendicular drawn from the centre of the ellipse x^{2}+3y^{2} =6 on any tangent to it is
(x^{2}-y^{2})^{2} = 6x^{2}+2y^{2}
(x^{2}-y^{2})^{2} = 6x^{2} -2y^{2}
(x^{2}+y^{2})^{2} = 6x^{2}+2y^{2}
(x^{2}+y^{2})^{2} = 6x^{2}+2y^{2}
The slope of the line touching both the parabolas y^{2} = 4x and x^{2}-32y is
1/2
3/2
1/8
1/8
A.
1/2
For parabola, y^{2} = 4x
Let y = mx + 1/m be tangent line and it touches the parabola x^{2}=-32y
The circle passing through (1,-2) and touching the axis of x at (3,0) also passes through the point
(-5,2)
(2,-5)
(5,-2)
(5,-2)
The equation of the circle passing through the foci of the ellipse and having centre at (0,3) is
x^{2}+y^{2}-6y-7 =0
x^{2}+y^{2}-6y+7 =0
x^{2}+y^{2}-6y-5 =0
x^{2}+y^{2}-6y-5 =0
Let Tn be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If T_{n+1} − T_{n} = 10, then the value of n is
7
5
10
10
Given A circle, 2x^{2} + 2y^{2}= 5 and parabola,
Statement I An equation of a common tangent to these curves is
Statement II If the line is the common tangent, then m satisfies m^{4}-3m^{2}+2 =0
Statement I is true, Statement II is true; Statement II is a correct explanation for statement I
Statement I is true, Statement II is true; Statement II is not a correct explanation for statement I
Statement I is true, Statement II is false
Statement I is true, Statement II is false
Statement I An equation of a common tangent to the parabola and the ellipse 2x^{2} +y^{2} =4 is .
Statement II If the line is a common tangent to the parabola and the ellipse 2x^{2} +y^{2} =4, then m satisfies m^{4} +2m^{2} =24
Statement 1 is false, statement 2 is true
Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1
Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1
Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1
The area bounded between the parabolas x^{2}=y/4 and x^{2} = 9y, and the straight line y = 2 is
If z ≠ 1 and is real, then the point represented by the complex number z lies
either on the real axis or on a circle passing through the origin
on a circle with centre at the origin
either on the real axis or on a circle not passing through the origin
either on the real axis or on a circle not passing through the origin
The length of the diameter of the circle which touches the x-axis at the point (1, 0) and passes through the point (2, 3) is
10/3
3/5
6/5
6/5