The tangents drawn from the origin to the circle $x^{2} + y^{2} - 2 r x - 2 h y + h^{2} = 0$ are perpendicular, if

h = \pm r

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

h = \pm 2 r

No worries! We‘ve got your back. Try BYJU‘S free classes today!

h^{2} + r^{2} = 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

h = \pm 3 r

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $h = \pm r$
The combined equation of the tangents that can be drawn from $(0, 0)$ to $x^{2} + y^{2} - 2 r x - 2 h y + h^{2} = 0$ , is
$S S_{1} = T^{2}$
$(x^{2} + y^{2} - 2 r x - 2 h y + h^{2}) h^{2} = (- r x - h y + h^{2})^{2}$
This equation represents a pair of perpendicular straight lines if
Coeff. of $x^{2}$ + Coeff. of $y^{2} = 0$
$\Rightarrow 2 h^{2} - r^{2} - h^{2} = 0 \Rightarrow r^{2} = h^{2}$
$\Rightarrow r = \pm h$
Ans: A

Suggest Corrections

Similar questions

The tangents drawn from the origin to the circle $x^{2} + y^{2} - 2 r x - 2 h y + h^{2} = 0$ are perpendicular then sum of all possible values of $\frac{h}{r}$ is ___

Q. Equation of tangent drawn from origin to the circle

x^{2} + y^{2} - 2 r x - 2 h y + h^{2} = 0

are:

Q. The equations of the tangents drawn from the origin to the circle

x^{2} + y^{2} - 2 r x - 2 h y + h^{2} = 0

are

Q. The equation of the tangents drawn from the origin to the circle

x^{2} + y^{2} - 2 r x - 2 h y + h^{2} = 0

are

Q. The equation of tangents drawn from the origin to the circle

x^{2} + y^{2} - 2 r x - 2 h y + h^{2} = 0

are

x = 0

and

(h^{2} - r^{2}) x - 2 r h y = 0

Join BYJU'S Learning Program

The tangents drawn from the origin to the circle x2+y2−2rx−2hy+h2=0 are perpendicular, if

The tangents drawn from the origin to the circle $x^{2} + y^{2} - 2 r x - 2 h y + h^{2} = 0$ are perpendicular, if