What is the equation of the line passing through the origin and perpendicular to the line?

If the line passes through the origin, then you know that (0,0) is on the line. If the line is perpendicular to y=2x+3 then we know the line has slope m=−0.5. This is the negative reciprocal of the slope. The solution can be obtained by solving y=−0.5x+b using the information given.

What is the equation of straight line passing through origin?

In general, therefore, the equation y = mx represents a straight line passing through the origin with gradient m. The equation of a straight line with gradient m passing through the origin is given by y = mx .

What is the joint equation of pair of lines passing through the origin?

The equation of a line with slope m is given by $y = mx + c$ . Here, both the lines pass through origin. So, $c = 0$ . Thus, equation of line passing through origin is $y = mx$ .

What is the condition that the lines represented by ax2 2hxy by2 0 may be perpendicular to each other?

Condition that the two lines represented by the equation ax2 + 2hxy + by2 = 0 to be perpendicular is. Given lines are perpendicular. Hence option (2) is the answer.

Which one line passes through the origin?

The slope intercept form is y = mx + b, where b is the y-intercept. In the equation y = 2x – 1, the y-intercept is -1. So, if you have an equation like y = 4x, there is no “b” term. Therefore, the y-intercept is zero, and the line passes through the origin.

Which of the following equation passes through the origin?

Any line passing through origin is of the form y = mx or ax + by = 0. Here in the given option, 2x – y = 0 is in the form ax + by = 0.

What is joint equation of pair?

The equation ax²+2hxy+by²+2gx+2fy+c=0 is known as the general equation of second degree. Thus, the joint equation of a pair of straight lines is general equation of second degree.

Which of the following is joint equation of plane?

xy=x+y.

What is the equation of a pair of straight lines?

Equation of pair of straight lines = (m1x – y) (m2x – y) = m1m2x2 – (m1 + m2)xy + y2 , which is a homogeneous 2nd degree equation.

What is homogeneous equation of straight line?

The homogeneous equation of pair of straight lines passing through the origin is given by. ax2+2hxy+by2=0.

Which equation represents a pair of straight lines passing through the origin?

(1) Equation of a pair of straight lines passing through origin: The equation ax 2 + 2hxy + by 2 = 0 represents a pair of straight line passing through the origin where a, h, b are constants. Hence, (a) The lines are real and distinct, if h 2 – ab > 0 (b) The lines are real and coincident, if h 2 – ab = 0

What is the joint equation of St lines passing through origin?

Hence the joint equation of the pair of st. lines passing through origin & which are perpendicular to the lines (1) is : bx^2 – 2h xy + ay^2 = 0 . This gives the required pair of st. lines passing through origin and perpendicular to the given lines .

What is the joint equation of two lines perpendicular to each other?

Now, lines perpendicular to the lines y = mx , y = m’x and passing through origin can be written as my + x = 0 and m’y + x = 0. Hence the joint equation of the pair of st. lines passing through origin & which are perpendicular to the lines (1) is : bx^2 – 2h xy + ay^2 = 0 .

What are pair of straight lines?

What are Pair of Straight Lines? The equation ax 2 + 2hxy + by 2 = 0 represents a pair of straight line passing through the origin where a, h, b are constants. where a, b, c, f, g, h are constants, is said to be a general equation of second degree in x and y.