If the image of the point `(x_1, y_1)` with respect to the mirror `ax+by+c=0` be `(x_2 , y_2)` then.
(a) `(x_2-x_1)/a = (a x_1 + b y_1+ c)/(a^(2)+b^(2))`
(b) `(x_2-x_1)/a = (y_2 - y_1)/b`
(c) `(x_2-x_1)/a = -2 ((a x_1 + b y_1+ c)/(a^(2)+b^(2)))`
(d) None of these

If y=(log)_e(x/a)^x ,then x^3y_2= (a) (xy_1-y)^2 (b) ((y-x y_1)/(y_1))^2 (c) none of these

Three points A(x_1 , y_1), B (x_2, y_2) and C(x, y) are collinear. Prove that: (x-x_1) (y_2 - y_1) = (x_2 - x_1) (y-y_1) .

If y=log_e(x/(a+b x))^x , then x^3y_2 is (a) (x y_1-y)^2 (b) (1+y)^2 (c) ((y-x y_1)/(y_1))^2 (d) none of these

The length of projection of the segment join (x_1,y_1,z_1) and (x_2,y_2,z_20 on te line (x-alpha)/l=(y-beta)/m=(z-gamma)/n is (A) |l(x_2-x_1)+m(y_2-y_1)+n(z_2-z_1) (B) |alpha(x_2-x_1)+beta(y_2-y_1)+gamma(z_2-z_1)| (C) |(x_2-x_1)/l+(y_2-y_1)/m+(z_2-z_1)/n| (D) none of these

If the point P(x ,\ y) is equidistant from A(5,\ 1) and B(-1,\ 5) , then (a) 5x=y (b) x=5y (c) 3x=2y (d) 2x=3y

If y=(sin^(-1)x)^2,\ then (1-x^2)y_2 is equal to x y_1+2 (b) x y_1-2 (c) x y_1+2 (d) none of these

The family of lines (2 cos theta + 3 sin theta) x + (3 cos theta - 5 sin theta) y-(5 cos theta - 2 sin theta) = 0 is concurrent at (x_1, y_1) and the family of lines (a+2b) x+(a-3b) y+b-a=0 for different values of a and b is concurrent at (x_2, y_2) then : (A) x_2 + y_2 = x_1 (B) x_2 + y_2 = y_1 (C) 6x_2 + y_2 = 2x_1 + y_1 (D) none of these

If y=sin(m\ sin^(-1)x) , then (1-x^2)y_2-x y_1 is equal to m^2y (b) m y (c) -m^2y (d) none of these

The normal at the point (1,1) on the curve 2y+x^2=3 is (A) x + y = 0 (B) x y = 0 (C) x + y +1 = 0 (D) x y = 0

The normal at the point (1,1) on the curve 2y+x^2=3 is (A) x - y = 0 (B) x y = 0 (C) x + y +1 = 0 (D) x y = 0