y^(2)=a(b^(2)-x^(2))

Solve the diffrential equations : (dy)/(dx)+sqrt((a^(2)-y^(2))/(b^(2)-x^(2)))=0

A tangent at a point on the circle x^(2)+y^(2)=a^(2) intersects a concentric circle C at two points P and Q. The tangents to the circle X at P and Q meet at a point on the circle x^(2)+y^(2)=b^(2). Then the equation of the circle is x^(2)+y^(2)=abx^(2)+y^(2)=(a-b)^(2)x^(2)+y^(2)=(a+b)^(2)x^(2)+y^(2)=a^(2)+b^(2)

Evaluate (y^(2))/(b^(2))-(x^(2))/(a^(2)) , where x= a tan theta and y = b sec theta

Evaluate (y^(2))/(b^(2))-(x^(2))/(a^(2)) , whre x=a tan theta and y= b sec theta .

The two conics y^(2)/b^(2)-x^(2)/a^(2)=1 and y^(2)=-b/ax intersect if and only if

Locus of centroid of the triangle whose vertices are (a cos t,a sin t),(b sin t-b cos t)and(1,0) where t is a parameter is: (3x-1)^(2)+(3y)^(2)=a^(2)-b^(2)(3x-1)^(2)+(3y)^(2)=a^(2)+b^(2)(3x+1)^(2)+(3y)^(2)=a^(2)+b^(2)(3x+1)^(2)+(3y)^(2)=a^(2)-b^(2)

Prove that the curve (x^(2))/(a^(2))+(y^(2))/(b^(2))=1(x^(2))/(a^(12))+(y^(2))/(b^(2))=1 intersect orthogonally if a^(2)-a^(2)=b^(2)-b^(2)

If a=(x)/(x^(2)+y^(2))=b=(y)/(x^(2)+y^(2)), then the value of (x+y) is

Slope of the common tangent to the ellipse (x^(2))/(a^(2)+b^(2))+(y^(2))/(b^(2))=1,(x^(2))/(a^(2))+(y^(2))/(a^(2)+b^(2))=1 is