(a) `a^2+b^2` (b) `a+b` (c) `a^2-b^2` (d) `sqrt(a^2+b^2)`

The length of perpendicular from the centre to any tangent of the ellipse x^2/a^2 + y^2/b^2 =1 which makes equal angles with the axes, is : (A) a^2 (B) b^2 (C) sqrt(a^2-b^2)/2) (D) sqrt((a^2 + b^2)/2)

Two parallel lines lying in the same quadrant make intercepts a and b on x and y axes, respectively, between them. The distance between the lines is (a) (ab)/sqrt(a^2+b^2) (b) sqrt(a^2+b^2) (c) 1/sqrt(a^2+b^2) (d) 1/a^2+1/b^2

In triangle A B C ,2a csin(1/2(A-B+C)) is equal to (a) a^2+b^2-c^2 (b) c^2+a^2-b^2 (c) b^2-c^2-a^2 (d) c^2-a^2-b^2

In any A B C , the value of 2a csin((A-B+C)/2) is (a) a^2+b^2-c^2 (b) c^2+a^2-b^2 (c) b^2-c^2-a^2 (d) c^2-a^2-b^2

If the equation (a^2+b^2)x^2-2(a c+b d)x+c^2+d^2=0 has equal roots, then (a) a b=c d (b) a d=b c (c) a d=sqrt(b c) (d) a b=sqrt(c d)

If acostheta-bsintheta=c , then asintheta+bcostheta= (a) +-sqrt(a^2+b^2+c^2) (b) +-sqrt(a^2+b^2-c^2) (c) +-sqrt(c^2-a^2-b^2) (d) None of these

The length of the perpendicular drawn from the point P(a , b , c) from z-axis is a. sqrt(a^2+b^2) b. sqrt(b^2+c^2) c. sqrt(a^2+c^2) d. sqrt(a^2+b^2+c^2)

If D is the mid-point of the side B C of triangle A B C and A D is perpendicular to A C , then 3b^2=a^2-c ^2 (b) 3a^2=b^2 3c^2 b^2=a^2-c^2 (d) a^2+b^2=5c^2

If tantheta=a/b , then (asintheta+bcostheta)/(asintheta-bcostheta) is equal to (a) (a^2+b^2)/(a^2-b^2) (b) (a^2-b^2)/(a^2+b^2) (c) (a+b)/(a-b) (d) (a-b)/(a+b)

In triangle A B C ,2a csin(1/2(A-B+C)) is equal to a^2+b^2-c^2 (b) c^2+a^2-b^2 b^2-c^2-a^2 (d) c^2-a^2-b^2