Chapter 6: Two dimensional Analytical Geometry

The equation of the locus of the point whose distance from y – axis is half the distance from origin is

(4) 3x² – y² = 0

Which of the following equation is the locus of (at², 2at)

(4) y² = 4ax

Which of the following points lie on the locus of 3x² + 3y² – 8x – 12y + 17 = 0

(3) (1, 2)

If the point (8, – 5) lies on the focus x²/16−y²/25 = k, then the value of k is

(4) 3

Straight line joining the points (2, 3) and (- 1, 4) passes through the point (α, β) if

(3) α + 3β = 11

The slope of the line which males an angle 45°with the line 3x – y = – 5 are

(2) 1/2, – 2

Equation of the straight line that forms an isosceles triangle with coordinate axes in the 1-quadrant with perimeter 4 + 2√2 is

(2) x + y – 2 = 0

The coordinates of the four vertices of a quadrilateral are (-2, 4), (-1, 2), (1, 2) and (2, 4) taken in order. The equation of the line passing through the vertex (-1, 2 ) and dividing the quadrilateral in the equal areas is

(4) x – y + 3 = 0

The intercepts of the perpendicular bisector of the line segment joining (1,2) and (3,4) with coordinate axes are

(2) 5, 5

The equation of the line with slope 2 and the length of the perpendicular from the origin equal to √5 is

(3) 2x - y = 5

If a line is perpendicular to the line Sx-y = 0 and forms a triangle with the coordinate axes of area 5 sq. units, then its equation is

(1) x + 5y ± 5√2 = 0

Equation of the straight line perpendicular to the line x – y + 5 = 0 through the point of intersection y-axis and the given line

(2) x + y – 5 = 0

If the equation of the base opposite to the vertex (2, 3) of an equilateral triangle is x + y = 2, then the length of a side is

(3) √6

The line (p + 2q)x + (p – 3q)y = p – q for different values of p and q passes through the point

(4) (2/5,3/5)

The point on the line 2x – 3y = 5 is equal distance from (1, 2), and (3, 4) is

(2) (4, 1)

The image of the point (2, 3) in the line y = -x is

(1) (- 3, – 2)

The length of perpendicular from the origin to the line x/3−y/4 = is

(3) 12/5

The y – intercept of the straight line passing through (1, 3) and perpendicular to 2x – 3y + 1 = 0 is

(2) 9/2

If the two straight lines x + (2k – 7)y + 3 = 0 and 3kx + 9y – 5 = 0 are perpendicular, then the value of k is

(1) k = 3

If a vertex of a square is at the origin and it’s one side lies along the line 4x + 3y – 20 = 0
then the area of the square is

(2) 16 sq. units

If the lines represented by the equation 6x² + 41xy – 7y² = 0 make angles α and β with x-axis then tan α . tan β =

(1) –6/7

The area of the triangle formed by the lines x² – 4y² = 0 and x = a is

(3) ½ a²

If one of the lines given by 6x² – xy – 4cy² = 0 is 3x + 4y = 0,then c equals to

(1) -3

θ is acute angle between the lines x² – xy – 6y² = 0 then 2cosθ+3sinθ / 4cosθ+5cosθ

(3) 5/9

The equation of one of the lines represented by the equation x² + 2xy cot θ – y² = 0 is

(4) x sin θ + y(cos θ + 1) = 0