The two circles which pass through `(0,a)a n d(0,-a)` and touch the line `y=m x+c` will intersect each other at right angle if (A) `a^2=c^2(2m+1)` (B) `a^2=c^2(2+m^2)` (C)`c^2=a^2(2+m^2)` (D) `c^2=a^2(2m+1)`

Medians of A B C intersect at G . If a r\ ( A B C)=27\ c m^2, then a r\ ( A B G C)= 6\ c m^2 (b) 9\ c m^2 (c) 12\ c m^2 (d) 18 c m^2

If a tangent of slope m' at a point of the ellipse passes through (2a,0) and if e denotes the eccentricity of the ellipse then (A)m^(2)+e^(2)=1(C)3m^(2)+e^(2)-1(B)2m^(2)+e^(2)=1 (D) none of these

The area of a circle is 220\ c m^2 . The area of a square inscribed in it is (a) 49\ c m^2 (b) 70\ c m^2 (c) 140\ c m^2 (d) 150\ c m^2

If the mean of a , b , c is M and a b+b c+c a=0 , then the mean of a^2, b^2, c^2 is M^2 (b) 3M^2 (c) 6M^2 (d) 9M^2

A line y=2x+c intersects the circle x^(2)+y^(2)-2x-4y+1=0 at P and Q. If the tangents at P and Q to the circle intersect at a right angle,then |c| is equal to

Joint equation of lines passing through the origin, and parallel to the lines y-m_(1)x+c_(1) and y=m_(1)x+c_(2) , is

Two sides of a triangle are y=m_(1)x and y=m_(2)x and m_(1),m_(2), are the roots of the equation x^(2)+ax-1=0. For all values of a, the orthocentre of the triangle lies at (A)(1,1) (B) (2,2) (C) ((3)/(2),(3)/(2)) (D) (0,0)

The point of intersection of tangents drawn to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the points where it is intersected by the line lx+my+n=0, is (A) ((-a^(2)l)/(n),(b^(2)m)/(n))(B)((-a^(2)l)/(m),(b^(2)n)/(m))(C)((a^(2)l)/(m),(-b^(2)n)/(m))(D)((a^(2)l)/(m),(b^(2)n)/(m))

Let the parabolas y=x(c-x) and y=x^(2)+ax+b touch each other at the point (1,0). Then a+b+c=0a+b=2b-c=1(d)a+c=-2

The area of a right isosceles triangle whose hypotenuse is 16sqrt(2)\ c m is 125 c m^2 (b) 158 c m^2 128 c m^2 (d) 144 c m^2