Which of the following pairs(s) of curves is/are orthogonal? `(a)` `y^2 = 4 a x` ; `y = ``e^ (-x/ (2 a))` `(b)` `y^2 = 4 a x` ; `x^2` `= ``4ay` ` ` `(c)` `xy = a^2 ` ; `x^2-y^2` `= ``b^2` `(d)` `y = a x` `;` `x^2`+`y^2` `= c^2 `

Which one of the following curves cut the parabola y^2 =4ax at right angles? x^2+y^2=a^2 (b) y=e^(-x//2a) y=a x (d) x^2=4a y

For which of the following values of m is the area of the regions bounded by the curve y=x-x^2 and the line y=m x equal 9/2? (a) -4 (b) -2 (c) 2 (d) 4

Which of the following is a point on the common chord of the circle x^2+y^2+2x-3y+6=0 and x^2+y^2+x-8y-13=0? (1,-2) (b) (1,4) (c) (1,2) (d) (1,-4)

Which of the following lines have the intercepts of equal lengths on the circle, x^2+y^2-2x+4y=0 (A) 3x -y= 0 (B) x+3y=0 (C) x+3y+10=0 (D) 3x-y-10=0

Find the angle of intersection of the curve x^2+y^2-4x-1=0 and x^2+y^2-2y-9=0 .

The locus of the midpoint of a chord of the circle x^2+y^2=4 which subtends a right angle at the origins is (a) x+y=2 (b) x^2+y^2=1 x^2+y^2=2 (d) x+y=1

The locus of a point, from where the tangents to the rectangular hyperbola x^2-y^2=a^2 contain an angle of 45^0 , is (a) (x^2+y^2)^2+a^2(x^2-y^2)=4a^2 (b) 2(x^2+y^2)^2+4a^2(x^2-y^(2))=4a^2 (c) (x^2+y^2)^2+4a^2(x^2-y^2)=4a^2 (d) (x^2+y^2)+a^2(x^2-y^(2))=a^4

Find the angle between the curves x^(2)-y^(2)= 2a^(2) and x^(2)+y^(2)=4a^(2)

Eliminate x and y from the following equations : a sin ^(2)+ b cos^(2) x=c, b sin ^(2) y+ a cos^(2) y=d, a tan x= b tan y .

Find the ordered pair (x ,y) for which x^2-y^2-i(2x+y)=2idot