Let PQR be a right-angled isosceles triangle, right angled at P(2,1)˙ If the equation of the line QR is 2x+y=3 , then the equation representing the pair of lines PQ and PR is (a) 3x2−3y2+8xy+20x+10y+25=0 (b) 3x2−3y2+8xy−20x−10y+25=0 (c) 3x2−3y2+8xy+10x+15y+20=0 (d) 3x2−3y2−8xy−15y−20=0
Prove that the product of the lengths of the perpendiculars drawn from the points (a2−b2,0)and (−a2−b2,0)to the line axcosθ+bysinθ=1is b2.
Find the equation of the line parallel to yaxis and drawn through the point of intersection of the lines x−7y+5=0and 3x+y=0.
Show that the equation of the passing through the origin and making an angle θwith the y=mx+cis xy=±1−mtanθm+tanθ.
If sum of the perpendicular distances of a variable point P(x,y)from the lines x+5y=0and 3x−2y+7=0is always 10. Show that P must move on a line.
The condition that one of the straight lines given by the equation ax2+2hxy+by2=0 may coincide with one of those given by the equation aprimex2+2hprimexy+bprimey2=0 is (abprime−aprimeb)2=4(haprime−hprimea)(bhprime−bprimeh) (abprime−aprimeb)2=(haprime−hprimea)(bhprime−bprimeh) (haprime−hprimea)2=4(abprime−aprimeb)(bhprime−bprimeh) (bhprime−bprimeh)2=4(abprime−aprimeb)(haprime−hprimea)