If parabolas `y^2=lambdax` and `25[(x-3)^2+(y+2)^2]=(3x-4y-2)^2` are equal, then the value of `lambda` is (a)9 (b) 3 (c) 7 (d) 6

If x+4y=14 is a normal to the curve y^2=alphax^3-beta at (2,3), then the value of alpha+beta is 9 (b) -5 (c) 7 (d) -7

If lambdax^(2)-10xy+12y^(2)+5x-16y-3=0 , represents a pair of straight lines, then the value of lambda is

If the curves y^2=6x , 9x^2+by^2=16 intersect each other at right angles then the value of b is: (1) 6 (2) 7/2 (3) 4 (4) 9/2

If the equation (5x-1)^2+(5y-2)^2=(lambda^2-2lambda+1)(3x+4y-1)^2 represents an ellipse, then find values of lambdadot

If 4(x-sqrt2)^(2)-lambda(y-sqrt3)^(2)=45 and (x-sqrt2)^(2)-4(y-sqrt3)^(2)=5 cut orthogonally, then integral value of lambda is ________.

If the focus of the parabola x^2-k y+3=0 is (0,2), then a values of k is (are) 4 (b) 6 (c) 3 (d) 2

If the lines 3x^(2)-4xy +y^(2) +8x - 2y- 3 = 0 and 2x - 3y +lambda = 0 are concurrent, then the value of lambda is

If the ordered pairs (x^(2) - 3x, y^(2) + 4y ) and (-2,5) are equal , then find x and y .