Point Slope Form of a Line

Q.

Find the equation of the line passing through (-3, 5) and perpendicular to the line through the points (2, 5) and (-3, 6).

Q. Find the equation of the line which passes through the point (–4, 3) with slope .

Q.

Find the equations of the lines which cut off intercepts on the axes whose sum and product are 1 and -6 respectively.

Q.

If y = 2x is a chord of the circle $x^2+y^2-10x=0$, find the equation of a circle with this chord as diameter.

Or

Find the equation of ellipse whose foci are (2, 3) and (- 2, 3) and whose semi-minor axis is $\sqrt{5}$

Q. The equation of the line passing through (3, 1) parallel to the line $y=2x+3$ is .

1. y = 2x - 5
2. x + 2y = 5
3. y = 2x + 1

Q.

Reduce the following equations into slope-intercept form and find their slopes and the y-intercepts.

(i) x + 7y = 0, (ii) 6x + 3y -5 = 0, (iii) y = 0

Q.

Find equation of the line passing through the point (2, 2) and cutting off intercepts on the axis whose sum is 9.

Q.

Equation of the straight line passing through the point of intersection of the lines $3x+4y=7,x-y+2=0$ and having slope $3$ is

1. 21x−7y+16=0

2. 21x−7y+12=0

3. 9x−3y+14=0

4. 9x−3y+5=0

Q.

A person standing at the junction (crossing) of two straight paths represented by the equations $2x-3y+4=0$ and $3x+4y-5=0$ wants to reach the path whose equation is $6x-7y+8=0$ in the least time. Find equation of the path that he should follow.

Q. Solve the following systems of linear inequations graphically:

(i) 2x + 3y ≤ 6, 3x + 2y ≤ 6, x ≥ 0, y ≥ 0
(ii) 2x + 3y ≤ 6, x + 4y ≤ 4, x ≥ 0, y ≥ 0
(iii) x − y ≤ 1, x + 2y ≤ 8, 2x + y ≥ 2, x ≥ 0, y ≥ 0
(iv) x + y ≥ 1, 7x + 9y ≤ 63, x ≤ 6, y ≤ 5, x ≥ 0, y ≥ 0
(v) 2x + 3y ≤ 35, y ≥ 3, x ≥ 2, x ≥ 0, y ≥ 0

Q.

A line through the point A(2, 0), which makes an angle of ${30}^{\circ }$ with the positive direction of x-axis is rotated about A in clockwise direction through an angle ${15}^{\circ }$. The equation of the straight line in the new position is

1. 

2. 

3. 

4. 

Q. 3. Locus of the middle point of the intercept on the line y=x+c made by the lines 2x+3y=5 and 2x+3y=8, c being a parameter, is

Q. Distance between the lines 5x + 3y − 7 = 0 and 15x + 9y + 14 = 0 is
(a) $\frac{35}{\sqrt{34}}$

(b) $\frac{1}{3\sqrt{34}}$

(c) $\frac{35}{3\sqrt{34}}$

(d) $\frac{35}{2\sqrt{34}}$

(e) 35

Q. The equation of the parabola whose focus is (1, −1) and the directrix is x + y + 7 = 0 is
(a) x² + y² − 2xy − 18x − 10y = 0
(b) x² − 18x − 10y − 45 = 0
(c) x² + y² − 18x − 10y − 45 = 0
(d) x² + y² − 2xy − 18x − 10y − 45 = 0

Q. The equation of the line passing through (1, 5) and perpendicular to the line 3x − 5y + 7 = 0 is
(a) 5x + 3y − 20 = 0
(b) 3x − 5y + 7 = 0
(c) 3x − 5y + 6 = 0
(d) 5x + 3y + 7 = 0

Q. A line passes through the point (2, 2) and is perpendicular to the line 3x + y = 3. Its y-intercept is
(a) $\frac{1}{3}$
(b) 2/3
(c) 1
(d) 4/3

Q. The equation of the circle passing through the point (1, 1) and having two diameters along the pair of lines x² − y² −2x + 4y − 3 = 0, is
(a) x² + y² − 2x − 4y + 4 = 0
(b) x² + y² + 2x + 4y − 4 = 0
(c) x² + y² − 2x + 4y + 4 = 0
(d) none of these

Q. Find the equation of the line passing through the point (−3, 5) and perpendicular to the line joining (2, 5) and (−3, 6).

Q. Find the equation of the line whose perpendicular distance from the origin is 5 units and angle made by the perpendicular with positive X-axis is 30 degree

Q. Find the equation of the line which passes though and is inclined with the x -axis at an angle of 75°.

Q. The equation of the parabola whose vertex is (a, 0) and the directrix has the equation x + y = 3a, is
(a) x² + y² + 2xy + 6ax + 10ay + 7a² = 0
(b) x² − 2xy + y² + 6ax + 10ay − 7a² = 0
(c) x² − 2xy + y² − 6ax + 10ay − 7a² = 0
(d) none of these

Q. 43.equation of circle touching the lines |x-2|+|y-3|=4

Q. Find the equation of the line perpendicular to x-axis and having intercept − 2 on x-axis.

Q. L is a variable line such that the algebraic sum of the distances of the points (1, 1), (2, 0) and (0, 2) from the line is equal to zero. The line L will always pass through
(a) (1, 1)
(b) (2, 1)
(c) (1, 2)
(d) none of these

Q. The equation of the line perpendicular to $y=3x+5$, passing through the point (-1, -2) is .

1. x+3y+7=0
2. y=3x+1
3. 2x+3y+8=0

Q. Show that the area of the triangle formed by the lines y = m₁ x, y = m₂ x and y = c is equal to $\frac{c^2}{4}\left(\sqrt{33}+\sqrt{11}\right),$ where m₁, m₂ are the roots of the equation $x^2+\left(\sqrt{3}+2\right)x+\sqrt{3}-1=0.$

Q. Find the equation of the straight line on which the length of the perpendicular from the origin is 2 and the perpendicular makes an angle α with x-axis such that sin α = $\frac{1}{3}$.

Q. The straight line $x+2y=1$ meets the coordinate axes at $A$ and $B$. A circle is drawn through $A,B$ and the origin. Then the sum of perpendicular distances from $A$ and $B$ on the tangent to the circle at the origin is :

1. $4\sqrt{5}$
2. $\frac{\sqrt{5}}{4}$
3. $2\sqrt{5}$
4. $\frac{\sqrt{5}}{2}$

Q. A variable line $L$ is drawn through $O(0,0)$ to meet $L_1:x-y-8=0$ and $L_2:x-y-16=0$ at points $A$ and $B$ respectively. A point $P$ is taken on $L$ such that $\frac{1}{4OP}=\frac{1}{OA}+\frac{1}{OB}$. Then the locus of $P$ is

1. $3x-3y=4$
2. $3x+3y-4=0$
3. $3x-3y=16$
4. $x=y$

Q. If two opposite vertices of a square are (1, 2) and (5, 8), find the coordinates of its other two vertices and the equations of its sides.