A line meets the coordinate axes at A(a, 0) a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the coordinates of $A$ be $(a, 0)$ and $B$ be $(0, b)$. The circumcircle of $	riangle OAB$ passes through $(0, 0)$,$(a, 0)$,and $(0, b)$.The

Vedclass · Accepted Answer

$m+n$

Vedclass · Answer

(C) Let the coordinates of $A$ be $(a, 0)$ and $B$ be $(0, b)$. The circumcircle of $	riangle OAB$ passes through $(0, 0)$,$(a, 0)$,and $(0, b)$.The equation of the circle is $x^2 + y^2 - ax - by = 0$.The tangent to this circle at the origin $(0, 0)$ is obtained by setting the first-degree terms to zero: $-ax - by = 0$,or $ax + by = 0$.The perpendicular distance $m$ from $A(a, 0)$ to the line $ax + by = 0$ is $m = \frac{|a(a) + b(0)|}{\sqrt{a^2 + b^2}} = \frac{a^2}{\sqrt{a^2 + b^2}}$.The perpendicular distance $n$ from $B(0, b)$ to the line $ax + by = 0$ is $n = \frac{|a(0) + b(b)|}{\sqrt{a^2 + b^2}} = \frac{b^2}{\sqrt{a^2 + b^2}}$.Adding these distances,we get $m + n = \frac{a^2 + b^2}{\sqrt{a^2 + b^2}} = \sqrt{a^2 + b^2}$.The diameter of the circle $x^2 + y^2 - ax - by = 0$ is given by $\sqrt{g^2 + f^2 - c} 	imes 2 = \sqrt{(-a/2)^2 + (-b/2)^2} 	imes 2 = \sqrt{\frac{a^2+b^2}{4}} 	imes 2 = \sqrt{a^2 + b^2}$.Thus,the diameter is $m + n$.

$A$ line meets the coordinate axes at $A(a, 0)$ and $B(0, b)$. If the perpendicular distances from $A$ and $B$ to the tangent drawn at the origin to the circumcircle of $\triangle OAB$ are $m$ and $n$ respectively,then the diameter of that circle is

Similar Questions

The area of a circle having the lines $3x - 4y + 4 = 0$ and $6x - 8y - 7 = 0$ as two of its tangents is:

The line $4x - 3y + 15 = 0$ intersects the circle $x^2 + y^2 - 6x - 8y = 0$ at two points $A$ and $B$. The maximum area of $\Delta ABC$,where $C$ is a point on the circumference of the circle,will be - .............. $sq. \ units$.

Let $PQ$ and $RS$ be the tangents at the extremities of the diameter $PR$ of a circle of radius $r$. If $PS$ and $RQ$ intersect at a point $X$ on the circumference of the circle,then $(PQ \cdot RS)$ is equal to

Let $A(3,5)$,$B(-2,-7)$ and $C(\alpha, \beta)$ be three points such that $\angle ACB$ is a right angle and the area of triangle $ABC$ is $\frac{82}{3}$ square units. Then the number of such points $C$ is

Let $C_1$ be the circle in the third quadrant of radius $3,$ that touches both coordinate axes. Let $C_2$ be the circle with centre $(1,3)$ that touches $C_1$ externally at the point $(\alpha, \beta)$. If $(\beta-\alpha)^2=\frac{m}{n}$,where $\operatorname{gcd}(m, n)=1$,then $m + n$ is equal to :

Vedclass Test Series

Exam Paper Generator

Online Exam Module