4x^(2)-25y^(4)

Consider the family of circles If in the 1st quadrant, the common tangent to a circle of this family and the ellipse 4x^(2)+25y^(2)=100 meets the co-ordinate axes at A and B, then show that the locus of mid point of AB is 4x^(2) + 25y^(2) = 4x^(2)y^(2)

Statement-I The line 4x-5y=0 will not meet the hyperbola 16x^(2)-25y^(2)=400 . Statement-II The line 4x-5y=0 is an asymptote ot the hyperbola.

Statement-I The line 4x-5y=0 will not meet the hyperbola 16x^(2)-25y^(2)=400 . Statement-II The line 4x-5y=0 is an asymptote ot the hyperbola.

Statement-I The line 4x-5y=0 will not meet the hyperbola 16x^(2)-25y^(2)=400 . Statement-II The line 4x-5y=0 is an asymptote ot the hyperbola.

Identify the type of conic section for each of the equations 1. 2x^(2) -y^(2) = 7 2. 3x^(2) +3 y^(2) -4x + 3y + 10 =0 3. 3x^(2) + 2y^(2) = 14 4. x^(2) + y^(2) + x-y=0 5. 11x^(2) -25y^(2) -44x + 50y - 256 =0 6. y^(2) + 4x + 3y + 4=0

If y = mx + 1 is a tangent to the hyperbola 4x^(2) - 25y^(2) = 100 , find the value of 25 m^(4) + 5m^(2) + 1 .

Find the equation of tangent to the hyperbola 16x^(2)-25y^(2)=400 perpendicular to the line x-3y=4.

Find the equation of tangent to the hyperbola 16x^(2)-25y^(2)=400 perpendicular to the line x-3y=4.