Question 20.12.1: Find the equation of the line drawn through the point of int......
Find the equation of the line drawn through the point of intersection of the lines 4 x-3 y+7=0 and 2 x+3 y+5=0 and passing through the point (-4,5) .
Step-by-Step
The equation of any line through the point of intersection of the given lines is of the form
\begin{aligned}& (4 x-3 y+7)+k(2 x+3 y+5)=0 \qquad \qquad …(i)\\ \\\Rightarrow \quad & (4+2 k) x+(3 k-3) y+(5 k+7)=0\end{aligned}
If it passes through the point (-4,5) , we have
\begin{aligned}& (4+2 k)(-4)+(3 k-3) \cdot 5+(5 k+7)=0 \\ \\\Rightarrow \quad & -16-8 k+15 k-15+5 k+7=0 \Rightarrow 12 k=24 \Rightarrow k=2 .\end{aligned}
Substituting k=2 in (i), we get
8 x+3 y+17=0 , which is the required equation.
Related Answered Questions
Question: 20.8.3
Verified Answer:
We have
\begin{aligned}\sqrt{3} x+y+2=0 \Ri...
Question: 20.12.6
Verified Answer:
The given lines are 2 x+3 y-4=0 a...
Question: 20.12.5
Verified Answer:
The equation of any line through the point of inte...
Question: 20.12.4
Verified Answer:
5 x-4 y+1=0 \Rightarrow y=\frac{5}{4} x...
Question: 20.12.3
Verified Answer:
5 x+4 y-20=0 \Rightarrow y=\frac{-5}{4} x+...
Question: 20.12.2
Verified Answer:
The given lines are 3 x+4 y-7=0 a...
Question: 20.11.5
Verified Answer:
Let the origin O be shifted to a ...
Question: 20.11.4
Verified Answer:
Let the origin O be shifted to th...
Question: 20.11.3
Verified Answer:
Let O^{\prime}(h, k) be the point...
Question: 20.11.2
Verified Answer:
Let the original coordinates be P(x, y) [/...