# 10th Maths Chapter 5 Coordinate Geometry Exercise 5.3

10th Standard Maths Chapter 5 Coordinate Geometry Exercise 5.3 Guide. TN SSLC Samacheer Kalvi Guide Chapter 5 Exercise 5.3 Book Back Answers & Solutions. 10th All Subject Guide – Click Here. Class 1 to 12 All Subject Book Back Answers – Click Here.

• (i) X-axis
• (ii) Y-axis

Solution:

Solution:
2(x – y) + 5 = 0
⇒ 2x – 2y + 5 =
⇒ 2y = 2x + 5

Solution:
θ = 30°

Solution:

Solution:

### 6. The hill in the form of a right triangle has its foot at (19, 3)The inclination of the hill to the ground is 45°. Find the equation of the hill joining the foot and top.

Solution:
θ = 45°
Coordinate of foot of hill = (19, 3) let equation of line be y = mx + c
m = tan θ = tan 45° = 1
⇒ y = x + c
Substituting y = 3 & x = 19, 3 = 19 + c ⇒ c = -16

### 7. Find the equation of a line through the given pair of points

(ii) (2, 3) and (-7, -1)
Solution:
(i) Equation of the line in two point form is

⇒ 9y – 27 = 4x – 8
⇒ 4x – 9y – 8 + 27 = 0
⇒ 4x – 9y + 19 = 0

### 8. A cat is located at the point(-6, -4) in XY plane. A bottle of milk is kept at (5, 11). The cat wishes to consume the milk traveling through the shortest possible distance. Find the equation of the path it needs to take its milk.

Solution:
A = (x1, y1) = (-6, -4)
B = (x2, y2) = (5, 11)

Shortest path between A and B is a line joining A and B.

Solution:

Solution:

### 11. You are downloading a song. The percent y (in decimal form) of mega bytes remaining to get downloaded in x seconds is given by y = -0.1x + 1.

• (i) graph the equation.
• (ii) find the total MB of the song.
• (iii) after how many seconds will 75% of the song gets downloaded?
• (iv) after how many seconds the song will be downloaded completely?

Solution:
(i) y = -0.1x + 1
when x = 0 ⇒ y = 1
when y = 0 ⇒ y = 10

(ii) Total MB of song can be obtained when time = 0
∴ x = 0
⇒ y = 1 MB
⇒ remaining % = 25% ⇒ y = 0.25
0.25 = -0. 1x + 1
⇒ 0.1x = 0.75
⇒ 7.5 seconds.

(iv) song will downloaded completely when , remaining % = 0 ⇒ y = 0
⇒ 0 = -0.1x + 1
⇒ x = 10
∴ 10 seconds

• (i) 4, -6
• (ii) −5, 3/4

Solution:

### 13. Find the intercepts made by the following lines on the coordinate axes,

• (i) 3x – 2y – 6 = 0
• (ii) 4x + 3y + 12 = 0

Solution:
(i) The given equation is
3x – 2y – 6 = 0
3x – 2y = 6
Divided by 6
3×6 – 2y6 = 66
x2 – y3 = 1 ⇒ x2 + y−3 = 1
(Comparing with xa + yb = 1)
∴ x intercept = 2; y intercept = -3

(ii) The given equation is
4x + 3y + 12 = 0
4x + 3y = -12
Divided by -12
4x−12 + 3y−12 = −12−12
x−3 + y−4 = 1
(Comparing with xa + yb = 1)
∴ x intercept = -3; y intercept = -4

### 14. Find the equation of a straight line

• (i) passing through (1, -4) and has intercepts which are in the ratio 2: 5
• (ii) passing through (-8, 4) and making equal intercepts on the coordinate axes

Solution:
(i) ratio of intercept = 2 : 5