In the figure given above, PA and PB are tangents to the circle from point P. How many real values of x exist such that the length of PA is x and length of PB is $x^{2} + 1$ ?

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

Open in App

Solution

Tangents from an external point to a circle are equal in length. So, the lengths of PA and PB are equal.
We know that $P A = x a n d P B = x^{2} + 1$
PA = PB
$x = x^{2} + 1$
$x^{2} - x + 1 = 0$
Now, this is a quadratic equation.
If we compare to the standard form $a x^{2} + b x + c = 0, a = 1, b = - 1 a n d c = 1.$
$b^{2} - 4 a c = (- 1)^{2} - 4 (1) (1) = 1 - 4 = - 3.$
Since $b^{2} - 4 a c < 0$ , the equation will have no real roots.
Hence, there are no real values that satisfy the given condition.

Suggest Corrections

Similar questions

In the figure given above, PA and PB are tangents to the circle from point P. How many real values of

x

exist such that the length of PA is

x

and length of PB is

x^{2} + 1

In the given figure, PA and PB are two tangents drawn from an external point P to a circle with centre C and radius 4 cm. If PA $⊥$ PB, then the length of each tangent is

(a) 3 cm (b) 4 cm (c) 5 cm (d) 6 cm

Q. In the figure given below, PA and PB are tangents to the circle from point P. Which of the following is the correct relation between PA and PB?

Join BYJU'S Learning Program

In the figure given above, PA and PB are tangents to the circle from point P. How many real values of x exist such that the length of PA is x and length of PB is x2+1?

In the figure given above, PA and PB are tangents to the circle from point P. How many real values of x exist such that the length of PA is x and length of PB is $x^{2} + 1$ ?