Which of the following pair(s) of curves is/are orthogonal? `y^2=4a x ; y=e^(-x/(2a))` `y^2=4a x ; x^2=4a ya t(0,0)` `x y=a^2; x^2-y^2=b^2` `y=a x ;x^2+y^2=c^2`

Which of the following pairs(s) of curves is/are orthogonal? y^2=4a x ; y=e^(-x/(2a)) y^2 = 4ax; x^2 = 4ay at (0,0) x y=a^2; x^2-y^2=b^2 y=a x ; x^2+y^2=c^2

Which of the following pair of graphs intersect? y=x^(2)-x and y=1y=x^(2)-2x and y=sin xy=x^(2)-x+1 and y=x-4

Show that the following set of curves intersect orthogonally: y=x^(3) and 6y=7-x^(2)x^(3)-3xy^(2)=-2 and 3x^(2)y-y=2x^(2)+4y^(2)=8 and x^(2)-2y^(2)=4

Which of the following points lie on the parabola x^(2)=4ay?x=at^(2),y=2at b.x=2at,y=at^(2) c.x=2at^(2),y= ast x=2at,y=at^(2)

Find the angle of intersection of the following curves : y^2=xa n dx^2=y y=x^2a n dx^2+y^2=20 2y^2=x^3a n dy^2=32 x x^2+y^2-4x-1=0a n dx^2+y^2-2y-9=0 (x^2)/(a^2)+(y^2)/(b^2)=1a n dx^2+y^2=a b x^2+4y^2=8a n dx^2-2y^2=2 x^2=27ya n dy^2=8x x^2+y^2=2xa n dy^2=x y=4-x^2a n dy=x^2

If x=10 and y=0.1, which of the following is the greatest? x^(2)+y^(2)( b) x^(2)-y^(2)( c) x^(2)backslash y^(2) (d) (x^(2))/(y^(2))

Suppose a x+b y+c=0 , where a ,ba n dc are in A P be normal to a family of circles. The equation of the circle of the family intersecting the circle x^2+y^2-4x-4y-1=0 orthogonally is (a)x^2+y^2-2x+4y-3=0 (b)x^2+y^2-2x+4y+3=0 (c)x^2+y^2+2x+4y+3=0 (d) x^2+y^2+2x-4y+3=0

y-1=m_1(x-3) and y - 3 = m_2(x - 1) are two family of straight lines, at right angled to each other. The locus of their point of intersection is: (A) x^2 + y^2 - 2x - 6y + 10 = 0 (B) x^2 + y^2 - 4x - 4y +6 = 0 (C) x^2 + y^2 - 2x - 6y + 6 = 0 (D) x^2 + y^2 - 4x - by - 6 = 0

The equation (s) of common tangents (s) to the two circles x^(2) + y^(2) + 4x - 2y + 4 = 0 and x^(2) + y^(2) + 8x - 6y + 24 = 0 is/are

A line intersects x-axis at A(2, 0) and y-axis at B(0, 4) . A variable lines PQ which is perpendicular to AB intersects x-axis at P and y-axis at Q . AQ and BP intersect at R . Image of the locus of R in the line y = - x is : (A) x^2 + y^2 - 2x + 4y = 0 (B) x^2 + y^2 + 2x + 4y = 0 (C) x^2 + y^2 - 4y = 0 (D) x^2 + y^2 + 2x - 4y = 0