Find the equations to the straight lines passing through the poin… - Vidyadip

Question

Find the equations to the straight lines passing through the point (2, 3) and inclined at and angle of 45° to the line 3x + y - 5 = 0.

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Answer

Here, $\text{x}_1=2,\text{y}_1=3,\alpha=45^\circ$ m = slope of line 3x + y - 5 = 0 $=\frac{-\text{coeff of x}}{\text{coeff of y}}=-3$ The equation of the required line are $\text{y}-\text{y}_1=\frac{-3-\tan45^\circ}{1+(-3)\tan45^\circ}(\text{x}-2)$ $\text{y}-3=\frac{-3-1}{1+(-3)(1)}(\text{x}-2)$ $\text{y}-3=\frac{-4}{2}(\text{x}-2)=2\text{x}-4$ $2\text{x}-\text{y}-1=0$ Also, $\text{y}-3=\frac{-3+\tan45^\circ}{1-(-3)\tan45}(\text{x}-2)$ $\text{y}-3=\frac{-3+1}{1+3}(\text{x}-2)$ $\text{y}-3=\frac{-2}{4}(\text{x}-2)=\frac{-\text{x}}{2}+1$ $\text{x}+2\text{y}-8$

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