If `ST` and `SN` are the lengths of subtangents and subnormals respectively to the curve `by^2 = (x + 2a)^3.` then `(ST^2)/(SN)` equals (A)`1` (B) `(8b)/27` (C) `(27b)/8` (D) `((4b)/9)`

Find the equation of tangent and normal the length of subtangent and subnormal of the circle x^(2)+y^(2)=a^(2) at the point (x_(1),y_(1)) .

A,B,C and D have position vectors a,b,c and d, respectively, such that a-b=2(d-c). Then,

If a variable tangent to the curve x^2y=c^3 makes intercepts a , bonx-a n dy-a x e s , respectively, then the value of a^2b is 27c^3 (b) 4/(27)c^3 (c) (27)/4c^3 (d) 4/9c^3

If A(2,2) , B(-4,-4) and C(5,-8) are the vertices of Delta ABC then the length of the median through C is . . . . . Units

If a,b,c,d ,e are +ve real numbers such that a+b+c+d+e=8 and a^2 + b^2 +c^2 + d^2 +e^2 = 16 , then the range of 'e' is

If a,b,c are non-zero real numbers, then the minimum value of the expression ((a^(8)+4a^(4)+1)(b^(4)+3b^(2)+1)(c^(2)+2c+2))/(a^(4)b^(2)) equals

If P(9a-2, -b) divides the join of A(3a+1, -3) and B(8a, 5) in the ratio 3 : 1 find the values of a and b.

If a=2hati+2hatj-8hatk and b=hati+2hatj-4hatk , then the magnitude of a+b is equal to

Let C be the curve y=x^3 (where x takes all real values). The tangent at A meets the curve again at Bdot If the gradient at B is K times the gradient at A , then K is equal to 4 (b) 2 (c) -2 (d) 1/4

The values of b and c for which the identity of f(x+1)-f(x)=8x+3 is satisfied, where f(x)=b x^2+c x+d , are