मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता ११ वी

Answer the following question: Find the distance of the origin from the line 12x + 5y + 78 = 0 - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Answer the following question:

Find the distance of the origin from the line 12x + 5y + 78 = 0

बेरीज

उत्तर

Let p be the perpendicular distance of origin from the line 12x + 5y + 78 = 0.

Here, a = 12, b = 5, c = 78

∴ p = `|"c"/sqrt("a"^2 + "b"^2)|`

∴ p = `|78/sqrt(12^2 + 5^2)|`

= `|78/sqrt(144 + 25)|`

= `78/13`

= 6 units

shaalaa.com
General Form of Equation of a Line
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 5: Straight Line - Miscellaneous Exercise 5 [पृष्ठ १२५]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Arts and Science) [English] 11 Standard Maharashtra State Board
पाठ 5 Straight Line
Miscellaneous Exercise 5 | Q II. (10) | पृष्ठ १२५

संबंधित प्रश्‍न

Find the slope, X-intercept, Y-intercept of the following line:

2x + 3y – 6 = 0


Write the following equation in ax + by + c = 0 form.

y = 2x – 4


Write the following equation in ax + by + c = 0 form.

y = 4


Write the following equation in ax + by + c = 0 form.

`x/3 - y/2` = 0


Show that lines x – 2y – 7 = 0 and 2x − 4y + 15 = 0 are parallel to each other


Show that lines x − 2y − 7 = 0 and 2x + y + 1 = 0 are perpendicular to each other. Find their point of intersection


If the line 3x + 4y = p makes a triangle of area 24 square unit with the co-ordinate axes then find the value of p.


Find the distance of the origin from the line 7x + 24y – 50 = 0


Find the distance between parallel lines 9x + 6y − 7 = 0 and 3x + 2y + 6 = 0


Find points on the line x + y − 4 = 0 which are at one unit distance from the line 4x + 3y – 10 = 0.


Find the equation of the line passing through the point of intersection of lines x + y − 2 = 0 and 2x − 3y + 4 = 0 and making intercept 3 on the X-axis


If A(4, 3), B(0, 0), and C(2, 3) are the vertices of ∆ABC then find the equation of bisector of angle BAC.


D(−1, 8), E(4, −2), F(−5, −3) are midpoints of sides BC, CA and AB of ∆ABC Find equations of sides of ∆ABC


D(−1, 8), E(4, −2), F(−5, −3) are midpoints of sides BC, CA and AB of ∆ABC Find co-ordinates of the circumcenter of ΔABC


O(0, 0), A(6, 0) and B(0, 8) are vertices of a triangle. Find the co-ordinates of the incenter of ∆OAB


Select the correct option from the given alternatives:

The equation of a line, having inclination 120° with positive direction of X−axis, which is at a distance of 3 units from the origin is


Answer the following question:

Find the distance of the origin from the line x = – 2


Answer the following question:

Which of the following lines passes through the origin?


Answer the following question:

Obtain the equation of the line which is parallel to the X−axis and making an intercept of 5 on the Y−axis.


Answer the following question:

Obtain the equation of the line which is parallel to the Y−axis and making an intercept of 3 on the X−axis.


Answer the following question:

Find the equation of the line which passes through the point of intersection of lines x + y − 3 = 0, 2x − y + 1 = 0 and which is parallel X-axis


Answer the following question:

Find the equation of the line which passes through the point of intersection of lines x + y + 9 = 0, 2x + 3y + 1 = 0 and which makes X-intercept 1.


Answer the following question:

Find the distance of the line 4x − y = 0 from the point P(4, 1) measured along the line making an angle of 135° with the positive X-axis


For the lines 5x + 2y = 8 and 5x - 2y = 7, which of the following statement is true?


The y-intercept of the line passing through A( 6, 1) and perpendicular to the line x - 2y = 4 is ______.


Let the straight line x = b divide the area enclosed by y = (1 - x)2, y = 0 and x = 0 into two parts R1(0 ≤ x ≤ b) and R2 (b ≤ x ≤ 1) such that `R_1 - R_2 = 1/4`. Then b equals ______ 


The equation 12x2 + 7xy + ay2 + 13x - y + 3 = 0 represents a pair of perpendicular lines. Then the value of 'a' is ______  


If a plane has x-intercept l, y-intercept m and z-intercept n, and perpendicular distance of plane from the origin is k, then _______.


If the distance of the point (1, 1, 1) from the origin is half its distance from the plane x + y + z + k = 0, then k = ______.


Find the distance of the origin from the line 7x + 24y – 50 = 0 is:


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×