Question 20.12.6: Find the equation of the line through the intersection of th......
Find the equation of the line through the intersection of the lines 2 x+3 y=4 and x-5 y+7=0 that has its x -intercept equal to -4 .
Step-by-Step
The given lines are 2 x+3 y-4=0 and x-5 y+7=0 .
The equation of any line through the intersection of the given lines is of the form
\begin{aligned}& (2 x+3 y-4)+k(x-5 y+7)=0\\ \\\Rightarrow \quad & (2+k) x+(3-5 k) y+(7 k-4)=0\qquad …(i)\end{aligned}If this line has x -intercept -4 , then the point (-4,0) lies on (i).
\begin{array}{l}\therefore \quad(2+k)(-4)+(7 k-4)=0 \Rightarrow -8-4 k+7 k-4=0\\ \\\Rightarrow \quad 3 k=12 \Rightarrow k=4 .\end{array}
Substituting k=4 in (i), we get
6 x-17 y+24=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: 20.12.5
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: 20.12.1
Verified Answer:
The equation of any line through the point of inte...
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) [/...