Question

Number of lines that can be drawn through the point (5, 2) at a distance of 5 units from (2, - 2) is

Answer 1

we have to find the no of lines that can be drawn through the point (5, 2) at a distance of 5 units from (2, -2).

solution : let slope of lines is m.

lines passing through the point (5, 2) are given by, (y - 2) = m(x - 5)

⇒y - 2 = mx - 5m

⇒mx - y - 5m + 2 = 0

now lines appear at 5 units distance from (2, -2).

so, |m(2) - (-2) - 5m + 2|/√(m² + 1) = 5

⇒|2m - 5m + 4|/√(m² + 1) = 5

⇒(- 3m + 4)² = 25(m² + 1)

⇒9m² + 16 - 24m = 25m² + 25

⇒16m² + 24m + 9 = 0

⇒(4m)² + 2(4m)(3) + (3)² = 0

⇒(4m + 3)² = 0

⇒m = -3/4

Here slope of line , m = -3/4 [only one value of m]

so only one line passing through the point (5, 2) at a distance of 5 units from (2, -2).

Therefore no of lines that can be drawn through the point (5, 2) at a distance 5 units from (2, -2) is 1.

Answer 2

Answer:

1

Step-by-step explanation:

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