Coordinate Geometry (2D & 3D)

Q1. If the equation ax²+2hxy+by²+2gx+2fy+c = 0

represents a pair of straight lines then...

• (a) abc+2fgh-af²-bg²-ch²=0

• (b)abc+fgh-af²-bg²-ch²=0

• (c) 2abc+fgh-af²-bg²-ch²=0

• (d) None of these

Q2.Condition that the equation hxy+gx-fy+c = 0

represents a pair of straight lines is...

• (a) ch=ah

• (b) fh=cg

• (c) ch=fg

• (d) fg=-ch

Q3.The length of the latus rectum

of the conic ... (l/r) = 1+e cos θ

• (a) l

• (b) 2l

• (c) l/2

• (d) None of these

Q4.The polar equation

r = 2 /(3 cos θ + 4 sin θ)

represents ...

• (a) A straight line

• (b) A hyperbola

• (c) A parabola

• (d) An ellipse

Q5.The co ordinates of the centre of the circle

r = a cos θ + b sin θ

are given by ...

• (a) √(a²+b²) /2

  & tan^-1 (b/a)

• (b) √(a²+b²) /2

  & tan^-1 (a/b)

• (c) √(a²+b²)

  & tan^-1 (b/a)

• (d) None of these

Q6.The line (l/r) = A cos θ + B sin θ

will touch the conic (l/r) = 1+ e cos θ if...

• (a) (A-e)²+B²=0

• (b) (A-e)²+B²=1

• (c) A²+(B-e)²=0

• (d) None of these

Q7.The equation of the normal at ( a cos Φ , b sin Φ)

to the ellipse (x²/a²)+(y²/b²) = 1 is...

• (a) ax cos Φ +by sin Φ = a²+b²

• (b) ax cos Φ - by sin Φ = a²- b²

• (c) ax sec Φ - by cosec Φ = a²-b²

• (d) ax sec Φ + by cosec Φ = a²+b²

Q8. If the straight line y=mx+c

touches the parabola y² = 4a(x+a) .

then c is equal to...

• (a) 2am+am³

• (b) am²+ (a/m²)

• (c) a/m

• (d) am+(a/m)

Q9. If the normals at the point (at²,2at)

meets the parabola again is (at₁²,2at₁) then...

• (a) t₁ = t+ (2/t)

• (b) t₁ = - t - (2/t)

• (c) tt₁ = -1

• (d) (t-t₁) t₁ = 1

Q10.The pole of the straight line 2x+y+12=0

with respect to the circle x²+y²-4x+3y-1=0

is the point ...

• (a) (1,2)

• (b) (-2,1)

• (c) (1,-2)

• (d) (-1,-2)

Answer explanation