The points $\left(0,\frac{8}{3}\right),\left(1,3\right)$ and $\left(82,30\right)$

Important Questions on Straight Line

EASY

Mathematics>Coordinate Geometry>Straight Line>Equation of a Straight Line in Various Forms

A straight line through origin $O$ meets the lines $3y=10-4x$and $8x+6y+5=0$ at points $A$ and $B$ respectively. Then, $O$ divides the segment $AB$ in the ratio

MEDIUM

Mathematics>Coordinate Geometry>Straight Line>Equation of a Straight Line in Various Forms

The equation of perpendicular bisectors of sides $AB$ and $AC$ of a $∆ ABC$ are $x-y+5=0$ and $x+2y=0$ respectively. If the coordinates of vertex $A$ are $\left(1, -2\right),$ then equation of $BC$ is

MEDIUM

Mathematics>Coordinate Geometry>Straight Line>Equation of a Straight Line in Various Forms

Two sides of a rhombus are along the lines, $x-y+1=0$ and $7x-y-5=0$ . If its diagonals intersect at $\left(-1, -2\right)$ , then which one of the following is a vertex of this rhombus ?

HARD

Mathematics>Coordinate Geometry>Straight Line>Equation of a Straight Line in Various Forms

A straight line $L$ at a distance of $4$ units from the origin makes positive intercepts on the coordinate axes and the perpendicular from the origin to this line makes an angle of $60°$ with the line $x+y=0.$ Then an equation of the line $L$ is:
Note: In actual JEE Main paper, two options were correct for this question. Hence, we have changed one option.

EASY

Mathematics>Coordinate Geometry>Straight Line>Equation of a Straight Line in Various Forms

If a straight line passing through the point $P\left(-3, 4\right)$ is such that its intercepted portion between the coordinate axes is bisected at $P$, then its equation is :

EASY

Mathematics>Coordinate Geometry>Straight Line>Equation of a Straight Line in Various Forms

Suppose that the points $\left(h,\hspace{0.17em}k\right),\hspace{0.17em}\left(1,\hspace{0.17em}2\right)$ and $\left(-3,\hspace{0.17em}4\right)$ lie on the line $L_1.$ If a line $L_2$ passing through the points $\left(h,\hspace{0.17em}k\right)$ and $\left(4,\hspace{0.17em}3\right)$ is perpendicular to $L_1,$ then $\frac{k}{h}$ equals:

EASY

Mathematics>Coordinate Geometry>Straight Line>Equation of a Straight Line in Various Forms

A line has slope $\mathrm{m}$ and $\mathrm{y}$-intercept 4. The distance between the origin and the line is equal to

MEDIUM

Mathematics>Coordinate Geometry>Straight Line>Equation of a Straight Line in Various Forms

If we reduce $3x+3y+7=0$ to the form $x\cos \alpha +y\sin \alpha =p$, then the value of $p$ is

HARD

Mathematics>Coordinate Geometry>Straight Line>Equation of a Straight Line in Various Forms

$O (0, 0), A (1, 2), B (3, 4)$ are the vertices of $∆OAB.$ The joint equation of the altitude and median drawn from $O$ is

HARD

Mathematics>Coordinate Geometry>Straight Line>Equation of a Straight Line in Various Forms

A square, of each side $2$, lies above the $x$-axis and has one vertex at the origin. If one of the sides passing through the origin makes an angle $30°$ with the positive direction of the $x$-axis , then the sum of the $x$-coordinates of the vertices of the square is$:$

EASY

Mathematics>Coordinate Geometry>Straight Line>Equation of a Straight Line in Various Forms

A line cuts off equal intercepts on the co-ordinate axes. The angle made by this line with the positive direction of X-axis is

HARD

Mathematics>Coordinate Geometry>Straight Line>Equation of a Straight Line in Various Forms

Let $PS$ be the median of the triangle with vertices $P(2,2), Q(6,-1)$ and $R(7,3)$. The equation of the line passing through $(1,-1)$and parallel to $PS$ is 

EASY

Mathematics>Coordinate Geometry>Straight Line>Equation of a Straight Line in Various Forms

The equation of the line passing through the point $(-3,7)$ with slope zero is

MEDIUM

Mathematics>Coordinate Geometry>Straight Line>Equation of a Straight Line in Various Forms

A rectangle is inscribed in a circle with a diameter lying along the line $3y=x+7.$ If the two adjacent vertices of the rectangle are $\left(-8, 5\right)$ and $\left(6, 5\right),$ then the area of the rectangle $($in sq. units$)$ is:

MEDIUM

Mathematics>Coordinate Geometry>Straight Line>Equation of a Straight Line in Various Forms

If the perpendicular bisector of the line segment joining the points $P(1,4)$ and $Q(k,3)$ has $y$-intercept equal to $-4$, then a value of $k$ is;

MEDIUM

Mathematics>Coordinate Geometry>Straight Line>Equation of a Straight Line in Various Forms

The larger of two angles made with the $X$-axis of a straight line drawn through $(1,2)$ so that it intersects the line $x+y=4$ at a point distant $\sqrt{6}/3$ from the point $(1,2)$ is

EASY

Mathematics>Coordinate Geometry>Straight Line>Equation of a Straight Line in Various Forms

Line joining the points $(0,3)$ and $(5,-2)$ is a tangent to the curve $y=\frac{ax}{1+x}$, then

MEDIUM

Mathematics>Coordinate Geometry>Straight Line>Equation of a Straight Line in Various Forms

Let $b, d>0$ . The locus of all points $P \left(r, \theta \right)$ for which the line $OP$ (where $O$ is the origin) cuts the line $r\sin \theta =b$ in $Q$ such that $PQ=d$ is

HARD

Mathematics>Coordinate Geometry>Straight Line>Equation of a Straight Line in Various Forms

Let $O=(0, 0);$ let $A$ and$B$  be points respectively on $x$-axis and $y$-axis such that $\angle OBA=60°$. Let $D$ be a point in the first quadrant such that $OAD$ is an equilateral triangle. Then the slope of $DB$ is

EASY

Mathematics>Coordinate Geometry>Straight Line>Equation of a Straight Line in Various Forms

The points $\left(0,\frac{8}{3}\right),\left(1,3\right)$ and $\left(82,30\right)$