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.

Two perpendicular tangents drawn to the ellipse (x^2)/(25)+(y^2)/(16)=1 intersect on the curve.

If there exists exactly one point of the line 3x+4y+25=0 from which perpendicular tangesnt can be brawn to ellipse (x^(2))/(a^(2))+y^(2)=1(agt1) ,

Number of perpendicular tangents that can be drawn on the ellipse (x^(2))/(16)+(y^(2))/(25)=1 from point (6, 7) is

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

The points on the ellipse (x^(2))/(2)+(y^(2))/(10)=1 from which perpendicular tangents can be drawn to the hyperbola (x^(2))/(5)-(y^(2))/(1) =1 is/are

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

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 1/3dot Statement 2 : For the condition given in statement 1, the given line must touch the circle x^2+y^2=a^2+1.

Statement 1: If there exist points on the circle x^2+y^2=a^2 from which two perpendicular tangents can be drawn to the parabola y^2=2x , then ageq1/2 Statement 2: Perpendicular tangents to the parabola meet at the directrix.

Number of point (s) outside the hyperbola x^(2)/25 - y^(2)/36 = 1 from where two perpendicular tangents can be drawn to the hyperbola is (are)

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