If the algebraic sum of the distances from th | vedclass

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

Question

(D) Let the equation of the variable line be $ax + by + c = 0$,where $a^2 + b^2 = 1$.The perpendicular distance from a point $(x_1, y_1)$ to the line

Vedclass · Accepted Answer

$(1,1)$

Vedclass · Answer

(D) Let the equation of the variable line be $ax + by + c = 0$,where $a^2 + b^2 = 1$.The perpendicular distance from a point $(x_1, y_1)$ to the line $ax + by + c = 0$ is given by $d = ax_1 + by_1 + c$.The algebraic sum of the distances from the points $(2,0)$,$(0,2)$,and $(1,1)$ is zero:$(2a + 0b + c) + (0a + 2b + c) + (1a + 1b + c) = 0$$3a + 3b + 3c = 0$$a + b + c = 0$Substituting $c = -(a + b)$ into the line equation:$ax + by - (a + b) = 0$$a(x - 1) + b(y - 1) = 0$This equation holds for all $a$ and $b$ if $x - 1 = 0$ and $y - 1 = 0$.Thus,the line always passes through the fixed point $(1,1)$.

If the algebraic sum of the distances from the points $(2,0)$,$(0,2)$,and $(1,1)$ to a variable straight line is zero,then the line passes through the fixed point:

Similar Questions

There are two candles of the same length and size. Both of them burn at a uniform rate. The first one burns in $5 \, hr$ and the second one burns in $3 \, hr$. Both the candles are lit together. After how many minutes is the length of the first candle $3$ times that of the other?

$A(2,0), B(0,2), C(-2,0)$ are three points. Let $a, b, c$ be the perpendicular distances from a variable point $P(x, y)$ onto the lines $AB, BC$ and $CA$ respectively. If $a, b, c$ are in arithmetic progression,then the locus of $P$ is

Find the fixed point through which the line $x(a + 2b) + y(a + 3b) = a + b$ always passes for all values of $a$ and $b$.

$A$ straight line passes through a fixed point $(h, k)$. The locus of the foot of the perpendicular drawn from the origin to this line is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module