Maharashtra State BoardHSC Science (Electronics) 11th
Advertisement Remove all ads

If points A(h, 0), B(0, k) and C(a, b) lie on a line then show that ah+bk = 1 - Mathematics and Statistics

Sum

If points A(h, 0), B(0, k) and C(a, b) lie on a line then show that `"a"/"h" + "b"/"k"` = 1

Advertisement Remove all ads

Solution

A (h, 0), B (0, k) and C (a, b) lie on a line.

∴ A, B, Care collinear.

∴ slope of AB = slope of BC

∴ `("k" - 0)/(0 - "h") = ("b" - "k")/("a" - 0)`

∴ `- "k"/"h" = ("b" - "k")/"a"`

∴ – ak = bh – hk

∴ ak + bh = hk

∴ `("ak" + "bh")/"hk"` = 1

∴ `"a"/"h" + "b"/"k"` = 1

which is the required condition.

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×