Statement 1 : There can be maximum two points on the line `p x+q y+r=0` , from which perpendicular tangents can be drawn to the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` Statement 2 : Circle `x^2+y^2=a^2+b^2` and the given line can intersect at maximum two distinct points.

Number of points from where perpendicular tangents can be drawn to the curve (x^(2))/(16)-(y^(2))/(25)=1 is

Let (p, q) be a point from which two perpendicular tangents can be drawn to the ellipse 9x^(2)+16y^(2)=144. if K=3p+4q then

Number of points from which two perpendicular tangents can be drawn to both the ellipses E_1: x^2/(a^2+2)+y^2/b^2=1 and E_2:x^2/a^2+y^2/(b^2+1)=1 is

Statement 1: If there is exactly one point on the line 3x+4y+5sqrt(5)=0 from which perpendicular tangents can be drawn to the ellipse (x^(2))/(a^(2))+y^(2)=1,(a>1), then the eccentricity of the ellipse is (1)/(3). Statement 2: For the condition given in statement 1,the given line must touch the circle x^(2)+y^(2)=a^(2)+1

Find the points on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))= 2 from which two perpendicular tangents can be drawn to the circle x^(2) + y^(2) = a^(2)

The two circles x^(2)+y^(2)=r^(2) and x^(2)+y^(2)-10x+16=0 intersect at two distinct points.Then