Question

How to answer these question ?

Answer 1

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`

Answer 2

`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.!

Answer 3

`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`