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TS EAMCET · Maths · Parabola

If ax2+2hxy+by2-82x+98y+144=0 is the equation of a parabola with focus (2, -3) and directrix 3x-2y+5=0, then ax2+2hxy+by2=0 represents

  1. A two lines making an angle π3 at origin
  2. B a conic with eccentricity ab
  3. C two perpendicular lines
  4. D two coincident lines
Verified Solution

Answer & Solution

Correct Answer

(D) two coincident lines

Step-by-step Solution

Detailed explanation

For parabola, PS=PN ⇒x-22+y+32=3x-2y+532+-22 ⇒13x2-4x+4+y2+6y+9=9x2+4y2+25-12xy-20y+30x ⇒4x2+9y2+12xy-82x+98y+144=0 Comparing with given parabola a=4, b=9, h=-6 Now, 4x2-12xy+9y2=0 ⇒2x-3y2=0 It represents two coincident lines.