Advertisements
Advertisements
प्रश्न
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.
उत्तर
Let the line 3x + 4y = p cuts the X and Y axes at points A and B respectively.
3x + 4y = p
∴ `(3"x")/"p" + (4"y")/"p"` = 1
∴ `"x"/("p"/3) + "y"/("p"/4)` = 1
This equation is of the form `"x"/"a" + "y"/"b"` = 1,
where a = `"p"/3` and b = `"p"/4`
∴ A ≡ (a, 0) = `("p"/3, 0)` and B ≡ (0, b) = `(0, "p"/4)`
∴ OA = `"p"/3` and OB = `"p"/4`
Given, A(ΔOAB) = 24 sq. units
∴ `|1/2 xx "OA" xx "OB"|` = 24
∴ `|1/2 xx "p"/3 xx "p"/4|` = 24
∴ p2 = 576
∴ p = ± 24
APPEARS IN
संबंधित प्रश्न
Find the slope, X-intercept, Y-intercept of the following line:
2x + 3y – 6 = 0
Find the slope, X-intercept, Y-intercept of the following line:
3x − y − 9 = 0
Find the slope, X-intercept, Y-intercept of the following line:
x + 2y = 0
Write the following equation in ax + by + c = 0 form.
y = 4
Write the following equation in ax + by + c = 0 form.
`x/2 + y/4` = 1
Find the co-ordinates of the orthocenter of the triangle whose vertices are A(3, –2), B(7, 6), C(–1, 2).
Show that lines 3x − 4y + 5 = 0, 7x − 8y + 5 = 0, and 4x + 5y − 45 = 0 are concurrent. Find their point of concurrence
Find the equation of the line whose X-intercept is 3 and which is perpendicular to the line 3x − y + 23 = 0.
Find the distance of the origin from the line 7x + 24y – 50 = 0
Find the distance of the point A(−2, 3) from the line 12x − 5y − 13 = 0
Find the distance between parallel lines 4x − 3y + 5 = 0 and 4x − 3y + 7 = 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 parallel to the X-axis and passing through the point of intersection of lines x + y − 2 = 0 and 4x + 3y = 10
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
Select the correct option from the given alternatives:
Distance between the two parallel lines y = 2x + 7 and y = 2x + 5 is
Answer the following question:
Find the distance of the origin from the line x = – 2
Answer the following question:
Obtain the equation of the line which is parallel to the Y−axis and 2 units to the left of it.
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 P(−1, 1) from the line 12(x + 6) = 5(y − 2)
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 3x2 - 4xy + y2 = 0 represent a pair of straight lines whose slopes differ by ______.
The length of the perpendicular from the origin on the line `(xsinalpha)/"b" - (ycosalpha)/"a" - 1 = 0` is ______.
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:
