Let PQR be an isosceles right angled 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
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B
3x2−3y2+8xy−20x−10y+25=0
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C
3x2−3y2+8xy+10x+15y+20=0
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D
3x2−3y2−8xy−10x−15y−20=0
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Solution
The correct option is B3x2−3y2+8xy−20x−10y+25=0 Let m be the slope of PQ, then tan45o=∣∣∣m−(−2)1+m(−2)∣∣∣ ⇒1=∣∣∣m+21−2m∣∣∣⇒±1=m+21−2m ⇒m=13 or m=3 As PR also makes ∠45o with RQ,
∴ The above two values of m are for PQ and PR. ∴ Equation of PQ is as follows:
y−1=−13(x−2) ⇒x+3y−5=0 and equation of PR is:
⇒2x−y−5=0 ∴ Combined equation of PQ and PR is (x−3y−5)(3x−y−5)=0 ⇒3x2−3y2+8xy−20x−10y+25=0