A line parallel to the straight line `2x-y=0` is tangent to the hypernola `x^(2)/(4)-(y^(2))/(2)=1` at the point (`x_(1),y_(1))` Then `x_(1)^(2)+5y_(1)^(2)` is equal to :

The distannce between the tangent to the hyperbola (x^(2))/(4)-(y^(2))/(3) =1 parallel to the line y=x +2 is

if the line y=2x+c be a tangent to the ellipse (x^(2))/(8)+(y^(2))/(4)=1, then c is equal to

A straight line parallel to the line 2x-y+5 =0 is also a tangent to the curve y^2=4x+5 . Then the point of contact is

If the straight line y=mx+1 be the tangent of the parabola y^(2)=4x at the point (1,2) then the value of m will be-

The equation of the line parallel to the tangent to the circle x^(2)+y^(2)=r^(2) at the point (x_(1),y_(1)) and passing through origin is

If the straight line y=my+1 be the tangent of the parabola y^2=4x at the point (1,2), then the value of m will be

If the line joining the points (-x_(1),y_(1)) and (x_(2),y_(2)) subtends a right angle at the point (1,1), then x_(1)+x_(2)+y_(2)+y_(2) is equal to

Find the equations of the tangent line to the curve: y = 2x^2 + 3y^2 = 5 at the point (1,1)

If a straight line passing through the focus of the parabola y^(2) = 4ax intersectts the parabola at the points (x_(1), y_(1)) and (x_(2), y_(2)) , then prove that x_(1)x_(2)=a^(2) .

From every point on the line x+y=4 ,tangents are drawn to circle x^(2)+y^(2)=4 .Then,all chord of contact passes through (x_(1),y_(1)),x_(1)+y_(1)=