L 1 : 3x + 4y + 8 = 0 L 2 : 2x + 7y – 1= 0
(i) If L 1 , L 2 represent the sires AB and AC of the isosceles triangle ABC with AB = AC = 2 then the co-ordinates of –
2x + 7y + 21 = 0 1/4
10x + 35y = 63 1/2
10x + 35y + 21 = 0 1
(ii) Equation of the line through B parallel to AC is 2x + 7y = 63 (iii) If D is the mid-point of BC and E is the mid-point of CA then DE is equal to – 2
Text Solution
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Ans.
(i)
Sol. L 1 and L 2 intersect at A (4, – 1)
Equation of a line through A is
= 
…(1)
co-ordinates of any point on this at a distance 2 from A is
(2 cos θ + 4, 2sin θ – 1)
If (1) represents L 1 = AB then
tan θ = – 3/4 sin θ = ± 3/5 cos θ = ± 4/5
Let cos θ = 4/5 sin θ = –3/5
co-ordinate of B (28/5, – 11/5)
(ii)
Sol. Equation is 2x + 7y = k passes through B (28/5, –11/5)
k = – 21/5
(iii)
Sol. D E = 1/2 AB = 1
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