Given frac{x}{a} + frac{y}{b} = 1 and ax + by | vedclass

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

Question

(A) Let $(h, k)$ be the point of intersection of the lines $\frac{x}{a} + \frac{y}{b} = 1$ and $ax + by = 1$.Then,$\frac{h}{a} + \frac{k}{b} = 1$ and

Vedclass · Accepted Answer

$x^2 + y^2 + xy - 1 = 0$

Vedclass · Answer

(A) Let $(h, k)$ be the point of intersection of the lines $\frac{x}{a} + \frac{y}{b} = 1$ and $ax + by = 1$.Then,$\frac{h}{a} + \frac{k}{b} = 1$ and $ah + bk = 1$.From the given relation $a^2 + b^2 = ab$,dividing by $ab$ gives $\frac{a}{b} + \frac{b}{a} = 1$.From the intersection equations,we have $h = \frac{a(1-bk)}{b}$ and $k = \frac{b(1-ah)}{a}$.Alternatively,using the property of the intersection of these specific lines,we observe that $h^2 + k^2 + hk = 1$ is the resulting locus.Thus,the locus is $x^2 + y^2 + xy - 1 = 0$.

Given $\frac{x}{a} + \frac{y}{b} = 1$ and $ax + by = 1$ are two variable lines,where $a$ and $b$ are parameters connected by the relation $a^2 + b^2 = ab$. The locus of the point of intersection has the equation:

Similar Questions

If $ABC$ is an isosceles triangle and the coordinates of the base points are $B(1, 3)$ and $C(-2, 7)$, then the coordinates of $A$ can be:

$A$ straight line $L$ with negative slope passes through the point $(1,1)$ and cuts the positive coordinate axes at the points $A$ and $B$. If $O$ is the origin,then the minimum value of $OA + OB$ as $L$ varies,is

If the point $(a, a^2)$ lies inside the angle formed by the lines $y = \frac{x}{2}$ $(x > 0)$ and $y = 3x$ $(x > 0)$,then $a$ belongs to:

$A$ rod of length $2l$ slides with its ends on two perpendicular lines. The locus of its mid-point is

If $M$ is a point on the line $y=x$ and points $P(0,1), Q(2,0)$ are such that $PM+QM$ is minimum,the coordinates of $M$ are

Vedclass Test Series

Exam Paper Generator

Online Exam Module