Condition that line xcos α + ysin α = p may touch circle {x^2} + {y^2} = {a^2} is

English

Gujarati

Hindi

10-1.Circle and System of Circles

easy

The condition that the line $x\cos \alpha + y\sin \alpha = p$ may touch the circle ${x^2} + {y^2} = {a^2}$ is

A

$p = a\cos \alpha $

B

$p = a\tan \alpha $

C

${p^2} = {a^2}$

D

$p\sin \alpha = a$

Solution

(c) According to question length of perpendicular on the line from the centre of circle is equal to the radius of the circle.

$OM $ = radius of circle

$\left| {\frac{{ – p}}{{\sqrt {{{\cos }^2}\alpha + {{\sin }^2}\alpha } }}} \right| = a$

==> $| – p|\; = a \Rightarrow {p^2} = {a^2}$.

Standard 11

Mathematics

Share

Similar Questions

If the line $x = k$ touches the circle ${x^2} + {y^2} = 9$, then the value of $k$ is

easy

The equation of circle which touches the axes of coordinates and the line $\frac{x}{3} + \frac{y}{4} = 1$ and whose centre lies in the first quadrant is ${x^2} + {y^2} – 2cx – 2cy + {c^2} = 0$, where $c$ is

medium

A circle with centre $'P'$ is tangent to negative $x$ & $y$ axis and externally tangent to a circle with centre $(-6,0)$ and radius $2$ . What is the sum of all possible radii of the circle with centre $P$ ?

normal

Equation of the pair of tangents drawn from the origin to the circle ${x^2} + {y^2} + 2gx + 2fy + c = 0$ is

normal

A circle passes through the points $(- 1, 1) , (0, 6)$ and $(5, 5)$ . The point$(s)$ on this circle, the tangent$(s)$ at which is/are parallel to the straight line joining the origin to its centre is/are :

normal