General Form of a Straight Line

Q.

The area of the triangle formed by the coordinate axes and a line is $6$ square units and the length of its hypotenuse is $5$ units. Find the equation of the line.

Q.

What are the points on the y - axis whose distance from the line $\frac{x}{3}+\frac{y}{4}=1$ is 4 units.

Q. Locus of the point z satisfying the equation |i z -1|+|z -i|=2 is

1. an ellipse
2. a straight line
3. a pair of straight lines
4. a circle

Q. If the equation of the locus of a point equidistant from the points $(a_1,b_1)and(a_2,b_2)is(a_1-a_2)x+(b_1-b_2)y+c=0$
then the value of c is

1. $\frac{1}{2}(a_2^2+b_2^2-a_1^2-b_1^2)$
2. $a_1^2+a_2^2+b_1^2-b_2^2$
3. $\frac{1}{2}(a_1^2+a_2^2-b_1^2-b_2^2)$
4. $\sqrt{a_1^2+b_2^2-a_2^2-b_2^2}$

Q. Find the locus of the point which is equidistant from the points A(0, 2, 3) and (2, -2, 1).

Q.

Find the set of values of $\lambda$ for which the
line $3x-4y+\lambda =0$ intersects the ellipse
$\frac{x^2}{16}+\frac{y^2}{a}=1$ at 2 distinct point.

1. $(-12\sqrt{2},12\sqrt{2})$

2. $(12,12\sqrt{2})$

3. $(-12,12\sqrt{2})$

4. $(-12,12)$

Q.

Find the equation of the ellipse, with major axis along the X-axis and passing through the points (4, 3) and (-1, 4)

Or

Find the equation of the circle pasing through the points (-3, 4), (-2, 0) and (1, 5)) find the coordinates of the centre and radius of the circle.

Q.

General equation of a straight line is:

1. Ax² + By² + C = 0

2. y = mx + c

3. 

4. Ax + By + C = 0

Q. Find the equation of a st line which passes through origin making an angle of 60 degree with x+ root 3y+3 root 3=0

Q.

Slope of the straight line $ax+by+c=0$ is $\frac{-a}{b}$. State whether it is true or false.

1. True

2. False

Q. The straight lines x + y = 0, 3x + y- 4 = 0 and x + 3y - 4 = 0 form a triangle which is

1. Isosceles
2. Equilateral
3. Right-angled
4. Scalene

Q. Equation of the hour hand at 4 O’ clock is

1. $\sqrt{3}x-y=0$
2. $x+\sqrt{3}y=0$
3. $\sqrt{3}x+y=0$
4. $x-\sqrt{3}y=0$

Q. Equation of the hour hand at 4 O’ clock is

1. $x-\sqrt{3}y=0$
2. $\sqrt{3}x-y=0$
3. $x+\sqrt{3}y=0$
4. $\sqrt{3}x+y=0$

Q.

The equation of the locus of foot of perpendiculars drawn from the origin to the line passing through a fixed point (a, b), is

1. 

2. 

3. 

4. 

Q.

The equation of the locus of foot of perpendiculars drawn from the origin to the line passing through a fixed point (a, b), is

1. 

2. 

3. 

4. 

Q.

For the equation $x^2$ - (a - 3) x + a = 0 (a ∈ R), find the values of 'a' such that exactly one root lies in between 1 and 2.

1. a (10, )

2. None of these

3. a (-, -1)

4. a (-, -10)

Q. If a, b, and c are in AP, then the straight line $ax+by+c=0$ will always pass through a fixed point whose coordinates are___

1. (1, 2)
2. (1, -2)
3. (-1, 2)
4. (2, 1)

Q. A man wants to cut three lengths from a single piece of board of maximum length 91cm. The second length is to be 3 cm longer than the shortest and third length is to be twice as long as the shortest. What are the possible lengths for the shortest board, if third piece is to be atleast 5cm longer than the second? Also, show the possible lengths on a graph paper in Ist quadrant.

Q.

Find the value of k for which the lines $3x+y=2,k+2y=3$ and $2x-y=3$ may intersect at a point.

Q.

Find the distance of the line 4x+7y+5=0
from the point (1, 2) along the line 2x-y=0

Q.

The solution to the inequality 2 < x and 3x< 9 is given by the graph

1. 

2. 

3. 

4. 

Q. The line $\frac{x}{a}+\frac{y}{b}=1$ cuts the axis at $A$ and $B$, another line perpendicular to $AB$ cuts the axes at$P,Q$respectively.Locus of points of intersection of $AQ$ and $BP$ is

1. $x^2+y^2+ax+by=0$
2. $x^2+y^2-ax-by=0$
3. $x^2+y^2-ax+by=0$
4. $x^2+y^2+ax-by=0$

Q. Let $a,b,c$ be real numbers with $a^2+b^2+c^2=1$ Show that the equation $\left|\begin{array}{ccc}ax-by-c& bx+ay& cx+a\\ bx+ay& -ax+by-c& cy+b\\ cx+a& cy+b& -ax-by+c\end{array}\right|$ = 0
represents a straight line.

Q. If $a,b,c$ are in A.P. and line $ax+by+c=0$ always passes through a fixed point $(h,k)$, then the equation of straight line perpendicular to the line $3x+y-2=0$ and passing through $(h,k)$is

1. $x-3y+5=0$
2. $x-3y-7=0$
3. $x-3y=0$
4. $x-3y-2=0$

Q.

Find the equation of the circle with radius 5 whose centre lies on x - axis and passes through the point (2, 3)

Q.

If sum of the perpendicular distances of a variable point P(x, y) form the lines $x+y-5=0$ and $3x-2y+7=0$ is always 10.
Show that P must move on a line.

Q. find the equation of the line whose slope = -2\5 and y intercept = -3

Q. Prove that the line y − x + 2 = 0 divides the join of points (3, −1) and (8, 9) in the ratio 2 : 3.

Q. In what ratio is the line joining the points (2, 3) and (4, −5) divided by the line passing through the points (6, 8) and (−3, −2).

Q. For specifying a straight line how many geometrical parameters should be known

1. 1
2. 2
3. 4
4. 3