If `(x-a)^(2)+(y-b)^(2)=r^(2)`, show that, `((1+y_(1)^(2))^((3)/(2)))/(y_(2))=-r`.

IF x^2+y^2=a^2 , show that, (1+y_1^2)^(3/2)/y_2=-a

If y= (tan^(-1)x)^(2) , show that (x^(2)+1)^(2) y_(2)+2x(x^(2)+1)y_(1)=2 .

If" " x^(2) + y^(2) = 1, "show that, "(3x - 4x^(3))^(2) + (3y - 4y^(3))^(2) = 1.

If the tangent to the curve x^(3)+y^(3)=a^(3) at the point (x_(1),y_(1)) intersects the curve again at the point (x_(2),y_(2)) , then show that, (x_(2))/(x_(1))+(y_(2))/(y_(1))+1=0 .

If sqrt(1-x^2)+sqrt(1-y^2)=a(x-y) ,show that dy/dx=sqrt((1-y^2)/(1-x^2))

IF y=3e^(2x)+2e^(3x) , show that, y_2-5y_1+6y=0 .

If sqrt(1 -x^2) + sqrt(1-y^2) = a(x-y), show that, (dy)/(dx) = sqrtfrac(1-y^2)(1-x^2)

If x=acos^3theta and y=asin^3theta show that, (1+y_1^2)^(3/2)/y_2=3asinthetacostheta

A(x_(1) y_(1)) and B(x_(2), y_(2)) are two given points on a circle. If the chord AB substends an angle theta at a point p on its circumferene, show that the equation of the circle is (x-x_(1)) (x-x_(2))+(y-y_(1))(y-y_(2))=+- cos theta [ (x-x_(1))(y-y_(2))-(x-x_(2))(y-y_(1))]

If the tangent at point P(h, k) on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 cuts the circle x^(2)+y^(2)=a^(2) at points Q(x_(1),y_(1)) and R(x_(2),y_(2)) , then the vlaue of (1)/(y_(1))+(1)/(y_(2)) is