The hyperbola `x^2 / a^2 - y^2 / b^2 = 1` passes through the point of intersection of the lines `x - 3sqrt5 y = 0` and `sqrt5 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 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.

If the hyperbola x^2/a^2-y^2/b^2=1 passes through the interesecting point of two straight lines x=3sqrt5 y and sqrt5x-2y=13 and the length of latus rectum is 4/3 unit,the find the co-ordinate of its focus.

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 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 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 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 line passing through the point of intersection of x + y = 2,x-y = 0 and is parallel to x + 2y =5 , is

If the parabola y^(2)=4ax passes through the point of intersection of the straight lines 3x+y+5=0 and x+3y-1=0, find the co-ordinates of its focus and the length of its latus rectum.

If the parabola y^(2) = 4 ax passes through the point of intersection of the straight lines 3x + y + 5 = 0 and x + 3y - 1 = 0 , find the coordinates of its focus and the length of its latus rectum .