Home
Class 12
MATHS
If p,q be the portions of the intercepts...

If p,q be the portions of the intercepts upon the coordinate axes by the tangent to the curve `x^((2)/(3))+y^((2)/(3))=a^((2)/(3))` at the point `(x_(1),y_(1))` thenprove that (p,q) lies on the circle `x^(2)+y^(2)=a^(2)`.

Promotional Banner

Similar Questions

Explore conceptually related problems

The slope of the tangent to the curve (y-x^(5))^(2)=x(1+x^(2))^(2) at the point (1, 3) is

Find the equation of the tangent at the specified points to each of the following curves. the curve x^((2)/(3))+y^((2)/(3))=a^((2)/(3))"at" (x_(1),y_(1))

If p_(1) and p_(2) be the lengths of the perpendiculars from the origin upon the tangent and normal respectively to the curve x^((2)/(3)) +y^((2)/(3)) = a^((2)/(3)) at the point (x_(1), y_(1)) , then-

If h and k be the intercept on the coordinates axes of tangent to the curve ((x)/(a))^((2)/(3))+((y)/(b))^((2)/(3))=1 at any point, on it, then prove that (h^(2))/(a^(2))+(k^(2))/(b^(2))=1

The slope of the tangent to the curve (y-x^5)^2=x(1+x^2)^2 at the point (1,3) is

If the tangent at any point of the curve x^((2)/(3))+y^((2)/(3))=a^((2)/(3)) meets the coordinate axes in A and B, then show that the locus of mid-points of AB is a circle.

Show that the lenght of the portion of the tangent to the curve x^(2/3)+y^(2/3)=a^(2/3) at any point of it, intercept between the coordinate axes is contant.

Show that the length of the portion of the tangent to the curve x^((2)/(3))+y^((2)/(3))=4 at any point on it, intercepted between the coordinate axis in constant.

The angle between the two tangents drawn from a point p to the circle x^(2)+y^(2)=a^(2) is 120^(@) . Show that the locus of P is the circle x^(2)+y^(2)=(4a^(2))/(3)

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 .