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How to answer these question ?

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3 Answers
May 25, 2018

Answer:

See explanation below

Explanation:

Given #x+py=q# we know that passes trough (1,2), then

#1+2p=q#

By other hand, we know that our line is perpendicular to #2x-y+7=0#

Lets check the slopes of both lines

Slope of first line: #y=-x/p+q/p#, so slope is #-1/p#

Slope of second line #y=2x+7#, so slope is #2#

We know that two perpendicular lines verifies #m·m´=-1#

With #m# and #m´# both slopes, Then #-1/p·2=-1#, then #p=2#

Finally #1+2p=q#; and #1+4=5=q#

Our line is #x+2y=5#

May 25, 2018

Answer:

# p=2, q=5#.

Explanation:

Let, the given lines be #l_1 : x+py=q and l_2 : 2x-y+7=0#.

Let the given point be #P=P(1,2)#.

Rewriting #l_1 : y=-1/p*x+1/p*q and l_2 : y=2x+7#, we find

that their respective slopes are #m_1=-1/p and m_2=2#.

Knowing that, #l_1 bot l_2," we must have, "m_1*m_2=-1#.

#:. -1/p*2=-1 rArr p=2#.

Further, #P(1,2) in l_1 : x+py=q and p=2#.

#rArr q=1+2(2)=1+4=5#.

Enjoy Maths.!

May 25, 2018

Answer:

#p=2, q=5#

Explanation:

In my old age I prefer avoiding explicitly writing the slope. The perpendicular family comes from swapping the coefficients on #x# and #y#, negating one. We set the constant to choose the family member through #(1,2).#

So the perpendicular to #2x - y = -7 # through #(1,2)# is

#x + 2y = 1(1) + 2(2) = 5 #

#p=2, q=5#