Prove that the two parabolas `y^2=4ax` and `x^2=4by` intersects at an angle of `tan^1[(3a^(1/3)b^(1/3))/(2(a^(2/3)+b^(2/3)))]`

Prove that two parabolas y_(2)=4ax "and" x^(2)=4by intersect (other than the origin ) at an angle of Tan^(-1)[(3a^(1//3)b^(1//3))/(2(a^(2//3)+b^(2//3)))] .

show that the common tangent to the parabola y^(2)=4ax "and" x^(2)=4by is xa^(1//3)+yb^(1//3)+a^(2//3)b^(2//3)=0.

show that the common tangent to the parabola y^(2)=4ax "and" x^(2)=4by is xa^(1//3)+yb^(1//3)+a^(2//3)b^(2//3)=0.

If the tangents to the parabola y^(2)=4ax at (x_(1),y_(1)),(x_(2),y_(2)) intersect at (x_(3),y_(3)) then

The parabolas y^(2)=4ac and x^(2)=4by intersect orthogonally at point P(x_(1),y_(1)) where x_(1),y_(1)!=0 provided (A)b=a^(2)(B)b=a^(3)(C)b^(3)=a^(2)(D) none of these

Prove that tan^(-1)""(3a^(2)x-x^(3))/(a^(3)-3ax^(2))=3tan^(-1)""x/a .

The parabolas y^2=4ax and x^2=4by intersect orthogonally at point P(x_1,y_1) where x_1,y_1 != 0 provided (A) b=a^2 (B) b=a^3 (C) b^3=a^2 (D) none of these

The parabolas y^2=4ax and x^2=4by intersect orthogonally at point P(x_1,y_1) where x_1,y_1 != 0 provided (A) b=a^2 (B) b=a^3 (C) b^3=a^2 (D) none of these

If the curves (x^(2))/(a^(2))+(y^(2))/(4)=1 and y^(3)=16x intersect at right angles, show that a^(2)=(4)/(3) .

The parabolas y^2=4ac and x^2=4by intersect orthogonally at point P(x_1,y_1) where x_1,y_1 != 0 provided (A) b=a^2 (B) b=a^3 (C) b^3=a^2 (D) none of these