**Equations of Lines Advanced Questions:**

Here we are going to see an example problem on the topic coordinate geometry.

**Question 1 :**

Find the equation of a line passing through the point of intersection of the lines 4x + 7y − 3 = 0 and 2x − 3y + 1 = 0 that has equal intercepts on the axes.

**Solution :**

First let us find the point of intersection of the lines 4x + 7y − 3 = 0 and 2x − 3y + 1 = 0

4x + 7y − 3 = 0 ------(1)

2x − 3y + 1 = 0 ------(2)

3(1) + 7(2)

12x + 21y − 9 = 0

14x − 21y + 7 = 0

---------------------

26x - 2 = 0

x = 2/26

x = 1/13

Let us apply the value of x in (1), we get

4(1/13) + 7y - 3 = 0

7y - 3 + (4/13) = 0

7y = 3 - (4/13)

7y = (39-4)/13

7y = 35/13

y = (35/13 x 7)

y = 5/13

So, the point of intersection of the given lines is (1/13, 5/13). Since the required line is having equal intercepts, a = b

(x/a) + (y/b) = 1

The line is passing through the point (1/13, 5/13)

((1/13)/a) + ((5/13)/a) = 1

(1/13a) + (5/13a) = 1

6/13a = 1

13a = 6

a = 6/13

Equation of the line :

(x/(6/13)) + (y/(6/13)) = 1

(13x + 13y)/6 = 1

13x + 13y = 6

13x + 13y - 6 = 0

**Question 2 :**

A person standing at a junction (crossing) of two straight paths represented by the equations 2x −3y + 4 = 0 and 3x + 4y −5 = 0 seek to reach the path whose equation is 6x −7y + 8 = 0 in the least time. Find the equation of the path that he should follow.

**Solution :**

The equation of the given lines are

2x −3y + 4 = 0 -----(1)

3x + 4y −5 = 0 -----(2)

6x −7y + 8 = 0 -----(3)

the person is standing at the junction of paths represented by the line (1) and (2)

By solving the (1) and (2), we get

4(1) + 3(2)

8x - 12y + 16 = 0

9x + 12y - 15 = 0

--------------------

17x + 1 = 0

x = -1/17

By applying the value of x in (1), we get

2(-1/17) - 3y + 4 = 0

-3y = -4 + (2/17)

-3y = (-68 + 2)/17

-3y = - 66/17

y = 66/17(3) = 22/17

Thus the person is standing at the point (-1/17, 22/17)

The person can reach path (3) is the least time if he takes along the perpendicular the line to (3) from the point (-1/17, 22/17)

Slope of the line (3)

m = - coefficient of x/coefficient of y

m = -6/7

Equation of the line passing through the point (-1/17, 22/17) and having the slope -6/7

Slope of the required line = 7/6

(y - y_{1}) = m(x - x_{1})

(y - (22/17)) = (7/6) (x + (1/17))

(17y - 22)/17 = (7/6)(17x + 1)/17

6(17y - 22) = 7(17x + 1)

102y - 132 = 119x + 7

119x + 102y + 132 - 7 = 0

119 x + 102y + 125 = 0

After having gone through the stuff given above, we hope that the students would have understood, "Equations of Lines Advanced Questions".

Apart from the stuff given in this section "Equations of Lines Advanced Questions", if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**