AB is a line segment moving between the axes | vedclass

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

Question

(B) Let $P(h, k)$ be any point on the locus. Let $A$ be on the $X$-axis and $B$ be on the $Y$-axis. Let $	heta$ be the angle that the line segment $A

Vedclass · Accepted Answer

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

Vedclass · Answer

(B) Let $P(h, k)$ be any point on the locus. Let $A$ be on the $X$-axis and $B$ be on the $Y$-axis. Let $	heta$ be the angle that the line segment $AB$ makes with the $X$-axis. From the geometry of the figure,in $	riangle PMA$,we have $\sin 	heta = \frac{k}{b}$,which implies $k = b \sin 	heta$. In $	riangle BNP$,we have $\cos 	heta = \frac{h}{a}$,which implies $h = a \cos 	heta$. Using the identity $\sin^2 	heta + \cos^2 	heta = 1$,we substitute the values: $(\frac{k}{b})^2 + (\frac{h}{a})^2 = 1$. Replacing $(h, k)$ with $(x, y)$,the equation of the locus is $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$.

$AB$ is a line segment moving between the axes such that '$A$' lies on $X$-axis and '$B$' lies on $Y$-axis. If $P$ is a point on $AB$ such that $PA=b$ and $PB=a$,then the equation of the locus of $P$ is

Similar Questions

$ABC$ is a variable triangle such that $A$ is $(1, 2)$,and $B$ and $C$ lie on the line $y = x + \lambda$ (where $\lambda$ is a variable). The locus of the orthocenter of triangle $ABC$ is:

If $P = (1, 0)$,$Q = (-1, 0)$,and $R = (2, 0)$ are three given points,then the locus of the points $S$ satisfying the relation $SQ^2 + SR^2 = 2 SP^2$ is :

The point $P$ is equidistant from $A(1, 3)$,$B(-3, 5)$,and $C(5, -1)$. Then $PA$ is equal to:

$A$ straight line moves such that the sum of the reciprocals of its intercepts on two perpendicular lines is constant. Then the line always passes through:

$A$ point moves in the $XY$-plane such that the sum of its distances from two mutually perpendicular lines is always equal to $3$. The area enclosed by the locus of that point is (in sq. units)

Vedclass Test Series

Exam Paper Generator

Online Exam Module