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Find those points on x-axis, each …

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Find those points on x-axis, each of which is at a distance of 5 units from the point A(5, -3).

Posted by Samarveer Singh 2 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Preeti Dabral 2 years, 11 months ago

Let the required point on the x-axis be P(x, 0). Then,
PA = 5 {tex}\Rightarrow{/tex}PA² =25
{tex}\Rightarrow{/tex} (x - 5)² + (0 + 3)² = 25
{tex}\Rightarrow{/tex} x²-10x + 25 + 9 =25 {tex}\Rightarrow{/tex}x² - 10x + 9 =0
{tex}\Rightarrow{/tex} x²- x - 9x + 9 = 0 {tex}\Rightarrow{/tex} x(x -1) -9(x - 1)=0
{tex}\Rightarrow{/tex}(x - 1) (x -9) =0 {tex}\Rightarrow{/tex} x - 1 =0 or x - 9 =0
{tex}\Rightarrow{/tex} x = 1 or x = 9.

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