[" The hyperbola "(x^(2))/(a^(2))-(y^(2))/(b^(2))=1" passes through the point of intersection of the lines "7x+13y-87=0" and "],[5x-8y+7=0" and its latus rectum is "(32sqrt(2))/(5)" .Find the equation of the hyperbola "]

The hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2)) = 1 passes through the point of intersection of the lines 7x + 13y - 87 = 0 and 5x - 8y + 7 = 0 and its latus rectum is (32sqrt(2))/(5) Find a and b.

The hyperbola x^2/a^2 - y^2/b^2 = 1 passes through the point of intersection of the lines 7x+ 13y-87=0 and 5x-8y+7=0 and its latus rectum is 32sqrt(2)/5 . Find a and b .

The hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 passes through the point of intersection of the lines,7x+13y-87=0&5x-8y+7=0 & the latus rectum is 32(sqrt(2))/(5). The value of 2(a^(2)+b^(2)) is :

The ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 passes through the point of intersection of the lines 7x + 13 y - 87 = 0 and 5x - 8y + 7 = 0 and its length of latus rectum is (32sqrt(2))/(5) , find a and b .

The ellipse x^2/a^2+y^2/b^2=1 passes through the point of intersection of the lines 7x+13y=87and 5x-8y+7=0and the length of its latus rectum is (32sqrt2)/5 units.Find the values of a and b.

The hyperbola (x^(2))/(a^(2)) - (y^(2))/(b^(2)) = 1 passes throught the point of intersection of the lines x - 3sqrt(5)y =0 and sqrt(5)x - 2y = 13 and the length of its latus rectum is (4)/(5) . Find the coordinates of its foci.

The hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 passes through the point of intersection of the lines x-3sqrt(5)y=0 and sqrt(5)x-2y=13 and the length of its latus rectum is (4)/(3) units.The coordinates of its focus are

The hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2)) = 1 passes through the point of intersection of the lines x + y = 3, 2x - 3y = 1. and its eccentricity is sqrt(3) , show that its length of latus rectum is 2sqrt(14) .

The hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2)) = 1 passes through the point (-3,2) and its eccentricity is sqrt((5)/(3)) , find the length of its latus rectum.

If the ellipse x^2/a^2+y^2/b^2=1 passes through the intersecting points of two straight lines 7x + 13y -87=0 and 5x -8y + 7 = 0 and the'length of its latus rectum is (32sqrt2)/5 then find the value of a and b and also find its eccentricity