(B) The distance $d$ of a point $(x, y)$ from the origin $(0, 0)$ is given by the formula $d = \sqrt{x^2 + y^2}$.Substituting the given coordinates $(

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(B) The distance $d$ of a point $(x, y)$ from the origin $(0, 0)$ is given by the formula $d = \sqrt{x^2 + y^2}$.Substituting the given coordinates $(b \cos \theta, b \sin \theta)$:$d = \sqrt{(b \cos \theta)^2 + (b \sin \theta)^2}$$d = \sqrt{b^2 \cos^2 \theta + b^2 \sin^2 \theta}$$d = \sqrt{b^2(\cos^2 \theta + \sin^2 \theta)}$Since $\cos^2 \theta + \sin^2 \theta = 1$,we get:$d = \sqrt{b^2(1)} = b$.

Class 11 Mathematics Straight Line System of co-ordinates, Distance between two points, Section formulae

Medium

The distance of the point $(b \cos \theta, b \sin \theta)$ from the origin is

A
$b \cot \theta$
B
$b$
C
$b \tan \theta$
D
$b \sqrt{2}$

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Class 11 Questions

Class 11

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Straight Line

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System of co-ordinates, Distance between two points, Section formulae

$P$ and $Q$ are points on the line joining $A,(-2, 5)$ and $B,(3, 1)$ such that $AP = PQ = QB$. Then the mid-point of $PQ$ is

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If the midpoint of the line segment joining the points $(5, a)$ and $(b, 7)$ is $(3, 5)$,find $(a, b)$.

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What is the square root of the sum of the squares of the lengths of the perpendiculars drawn from the point $(-3, 4)$ to both axes?

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In what ratio does the $x$-axis divide the line segment joining the points $(3, -4)$ and $(-5, 6)$?

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The coordinates of a point are $(0, 1)$ and the ordinate of another point is $-3$. If the distance between the two points is $5$,then the abscissa of the other point is:

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The distance of the point $(b \cos \theta, b \sin \theta)$ from the origin is

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$P$ and $Q$ are points on the line joining $A,(-2, 5)$ and $B,(3, 1)$ such that $AP = PQ = QB$. Then the mid-point of $PQ$ is

If the midpoint of the line segment joining the points $(5, a)$ and $(b, 7)$ is $(3, 5)$,find $(a, b)$.

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In what ratio does the $x$-axis divide the line segment joining the points $(3, -4)$ and $(-5, 6)$?

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