If the straight line `xcosalpha+ysinalpha=p` touches the curve `(x^2)/(a^2)-(y^2)/(b^2)=1,` then prove that `a^2cos^2alpha-b^2sin^2alpha=p^2dot`

The line p=x cos alpha+y sin alpha becomes tangent to (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 if

If the line lx+my+n=0 touches the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 . Then

If xcosalpha+ysinalpha=4 is tangent to (x^(2))/(25)+(y^(2))/(9)=1 then the value of alpha is

If the line y cos alpha=x sin alpha+a cos alpha be a tangtnt to the circle x^(2)+y^(2)=a^(2) then

If straight line lx + my + n=0 is a tangent of the ellipse x^2/a^2+y^2/b^2 = 1, then prove that a^2 l^2+ b^2 m^2 = n^2.

If the pair of straight lines Ax^(2)+2Hxy+By^(2)=0 be conjugate diameters of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 , then prove that Aa^(2)=Bb^(2).

The straight line x+y=-sqrt2P will touch the hyperbola 4x^2-9y^2=36 if

The number of values of c such that the line y=4 x+c touches the curve (x^(2))/(4)+y^(2)=1 is

Find the maximum area of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 which touches the line y=3x+2.

If (x^(2)+y^(2))(a^(2)+b^(2))=(ax+by)^(2) , prove that x/a = y/b .