" 7."(x^(2))/(a^(2))+(y^(2))/(b^(2))=1

The coordinates of the point at which the line 3x+4y=7 is a normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1, are

If a point (x_(1),y_(1)) lies in the shaded region (x^(2))/(a^(2))-(y^(2))/(b^(2))=1, shown in the figure,then (x^(2))/(a^(2))-(y^(2))/(b^(2))<0 statement 2: If P(x_(1),y_(1)) lies outside the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1, then (x_(1)^(2))/(a^(2))-(y_(1)^(2))/(b^(2))<1

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 :

If (x)/(a)-(y)/(b) tan theta =1 and (x)/(a) tan theta +(y)/(b)=1 , then the value of (x^(2))/(a^(2))+(y^(2))/(b^(2)) is

Statement 1:If a point (x_1,y_1) lies in the shaded region (x^2)/(a^2)-(y^2)/(b^2)=1 , shown in the figure, then (x^2)/(a^2)-(y^2)/(b^2)<0 Statement 2 : If P(x_1,y_1) lies outside the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , then (x_1^ 2)/(a^2)-(y_1 ^2)/(b^2)<1

If a point (x_1,y_1) lies in the shaded region (x^2)/(a^2)-(y^2)/(b^2)=1 , shown in the figure, then (x^2)/(a^2)-(y^2)/(b^2)<0 Statement 2 : If P(x_1,y_1) lies outside the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , then (x1 2)/(a^2)-(y1 2)/(b^2)<1

If x/a costheta+y/b sintheta=1 and x/a sintheta-y/bcostheta=1 Prove that : (x^2)/(a^2)+(y^2)/(b^2)=2

Find the product.(i) (5-2x)(3+x) (ii) (x+7y)(7x-y)( iii) (a^(2)+b)(a+b^(2))( iv) (p^(2)-q^(2))(2p+q)