Statement-1: Tangents drawn from any poi...

Statement-1: Tangents drawn from any point on the circle `x^(2)+y^(2)=25` to the ellipse `(x^(2))/(16)+(y^(2))/(9)=1` are at right angle Statement-2: The locus of the point of intersection of perpendicular tangents to an ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` is its director circle
`x^(2)+y^(2)=a^(2)+b^(2)`.

Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1

Statement-1 is True, Statement-2 is True, Statement -2 is not a correct explanation for Statement-1

Statement-1 is True, Statement-2 is False.

Statement-1 is False, Statement-2 is True

Text Solution

Verified by Experts

The correct Answer is:

Statement-2 true (see Section 11 on page 25.16) Clearly. `x^(2)+y^(2)=25` is the director circle of the ellipse `(x^(2))/(16)+(y^(2))/(9)=1` So, tangents drawn from any point on `x^(2)+y^(2)=25` to the ellipse are at right angle. So, statement-1 is true. Also, statement-2 is correct explanation fro statement-1`.

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The locus of point intersection of perpendicular tangents of ellipse ((x-1)^(2))/(16)+((y-1)^(2))/(9)=1 is

`x^(2)+y^(2)=25`

`x^(2)+y^(2)+2x+2y-23=0`

`x^(2)+y^(2)-2x-2y-23=0`

none of these

the locus of the point of intersection of tangents to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 which meet at right , is

a circle

a parabola

an ellipse

a hyperbola

The locus of the point of intersection of perpendicular tangents to the circles x^(2)+y^(2)=a^(2) and x^(2)+y^(2)=b^(2) , is

`x^(2)+y^(2)=a^(2)-b^(2)`

`x^(2)+y^(2)=a^(2)+b^(2)`

`x^(2)+y^(2)=(a+b)^(2)`