The points on the x-axis whose perpendicular distance from the li… - Vidyadip

MCQ

The points on the $x$-axis whose perpendicular distance from the line $\frac{x}{a} + \frac{y}{b} = 1$ is a, are

✓
$\left[ {\frac{a}{b}(b \pm \sqrt {{a^2} + {b^2}} ),\,0} \right]$
B
$\left[ {\frac{b}{a}(b \pm \sqrt {{a^2} + {b^2}} ),\,0} \right]$
C
$\left[ {\frac{a}{b}(a \pm \sqrt {{a^2} + {b^2}} ),\,0} \right]$
D
None of these

✓

Answer

Correct option: A.

$\left[ {\frac{a}{b}(b \pm \sqrt {{a^2} + {b^2}} ),\,0} \right]$

a
(a) Let the point be $(h,0)$, then $a = \pm \frac{{bh + 0 - ab}}{{\sqrt {{a^2} + {b^2}} }}$

==> $bh = \pm a\sqrt {{a^2} + {b^2}} + ab \Rightarrow h = \frac{a}{b}(b \pm \sqrt {{a^2} + {b^2}} )$

Hence the point is $\left\{ {\frac{a}{b}(b \pm \sqrt {{a^2} + {b^2}} ),0} \right\}$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from 9. straight line→9. straight line — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $Z_1$ and $Z_2$ be any two complex number.

Statement $1:$ $\left| {{Z_1} - {Z_2}} \right|\, \ge \left| {{Z_{_1}}} \right|\, - \,\left| {{Z_{_2}}} \right|$

Statement $2:$ $\left| {{Z_1} + {Z_2}} \right|\, \le \left| {{Z_{_1}}} \right|\, + \,\left| {{Z_{_2}}} \right|$

$C$ the centre of the hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$. The tangents at any point $P$ on this hyperbola meets the straight lines $bx - ay = 0$ and $bx + ay = 0$ in the points $Q$ and $R$ respectively. Then $CQ\;.\;CR = $

$(x-1)^4+4(x-1)^3+6(x-1)^2+4(x-1)+1=$

The mean of 6 numbers is 42 If one number is excluded, the mean of remaining numbers is 45. Find the excluded number:

Choose the correct answer. What is the length of foot of perpendicular drawn from the point P(3, 4, 5) on y-axis.

A dice marked with digit $\{1, 2, 2, 3, 3, 3\} ,$ thrown three times, then the probability of getting sum of number on face of dice is six, is equal to :-

If $\mathrm{z}$ is a complex number, then the number of common roots of the equation $z^{1985}+z^{100}+1=0$ and $z^3+2 z^2+2 z+1=0$, is equal to :

The focal chord of the parabola $(y\ -2)^2 = 16(x\ -1)$ is a tangent to the circle $x^2 + y^2 -14x -4y + 51 = 0$ , then slope of the focal chord can be

The equation of the line passing through $(1, 1)$ and parallel to the line $2x + 3y - 7 = 0$ is

If $\mathrm{S}=\{\mathrm{a} \in \mathrm{R}:|2 \mathrm{a}-1|=3[\mathrm{a}]+2\{\mathrm{a}\}\}$, where $[\mathrm{t}]$ denotes the greatest integer less than or equal to $t$ and $\{t\}$ represents the fractional part of $t$, then $72 \sum_{\mathrm{a} \in \mathrm{S}} \mathrm{a}$ is equal to....................