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Find the equation of the line in slope intercept form that is perpendicular to 2x+3y-12=0 and passes through the point (-3, -5). show your work

 Jul 25, 2020
 #1
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Find the slope, m ,  of the given line.....do you know how to do that?

 

PERPINDICULAR slope will be  - 1/m

 

then     use the line form    y = -1/m x + b      sub in the x,y point given to calulate 'b'

 Jul 25, 2020
 #2
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The equation of the circle is x2+y2=4x2+y2=4. Thus, the centre of the circle is (0,0)(0,0) and radius is 2.

Since the line y=x+n⇒x−y+n=0y=x+n⇒x−y+n=0 is a tangent, the perpendicular distance from the point (0,0) to the tangent will be 2.

Thus, we get:
∣∣x−y+n2√∣∣=2|x−y+n2|=2

⇒∣∣0−0+n2√∣∣=2⇒|0−0+n2|=2

⇒n=±22–√⇒n=±22

Thus the two tangent equations are y=x±22–√y=x±22.

 Jul 25, 2020

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