Let the meeting point of the perpendicular lines be (a,b)
/OP/=(a2+b2)=7 ..... (i)
a2+b2=49
2x+3y=1 ;y=−(32)x+31
Gradient =−(32)
For perpendicular lines,the product of Gradient I and gradient II hence gradient II =23
Gradient=ΔxΔy
23=a−0b−0
2b=3a .... (ii)
Substituting (ii) in (i) ;
a2+(23a)2=49
4a2+9a2=196
a =4 or −4; b=6 or − 6.
To get the equation, we take the point (4,6) and the gradient 23
23=x−4y−6
2y-12=3x -12
2y=3x
When a=− 4 and b=−6
23=x−(−4)y−(−6)
3x+ 12=2y+12
2y=3x
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